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Valleytronic Properties in 2D materials Yoshi Iwasa, Univ. Tokyo & RIKEN MPI-UBC-UT Winter School on Quantum Materials Feb 16, 2018 University of Tokyo
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Page 1: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Valleytronic Properties in 2D materials

Yoshi Iwasa Univ Tokyo amp RIKEN

MPI-UBC-UT Winter School

on Quantum Materials

Feb 16 2018University of Tokyo

SARPES M Sakano K Ishizaka (Tokyo) S Shin K Yaji (ISSP) K Miyamoto T Okuda (Hiroshima)

High magnetic field measurements Y Kohama M Tokunaga (ISSP)

Theory T Oka (Dresden) M S Bahramy (Tokyo) Y YanaseY Nakamura (Kyoto)

Acknowledgements

Univ Tokyo Iwasa group

1 Introduction 2D materials Valley degree of freedom in TMDs

2 Valleytronics Valley Hall effect Circularly polarized light source

3 Superconductivity with spin-valley locking Enhanced Hc2 by SOI

Contents

n2D (cmndash2)

109 1011 1013 1015107

semiconductorinsulator

Si MOS-FET

metal

Interface

(GaAsAlGaAs)He surface

2D Electron Systems

httpwww2warwickacukfacsciphysicscurrenthttpsenwikipediaorgwiki2DEGhttpphysorgnews2011-02-

microwave-photons-nul

Electrochemical

Interfaces

2D crystalInterfaces

(LAOSTO

FeSeSTO)

2D Electron Systems rarr 2D Materials

Scotch Tape

CVD

MBE electrolyte

Family of 2D crystalline systems

Eg ( eV )

TMD (MX2)

M Mo W Ta hellip

XS Se Te

72 eV

(indirect)

06~23 eV

depending on

of layers

~2 eV (monolayer)

~03 eV (bulk)

Black PhosphorusGraphene

0 eV

h-BN

Valleytronics

Valley as information carriers

Candidate materialsSiDiamondAlAsBigraphene

ChallengeSearch for valley selective external perturbation

Direct gap in monolayer MoS2

Bulk Monolayer

Splendiani et al Nano Lett (2010)

4-layer 2-layer

Cao et al Nat Comm (2012)

Mak et al Phys Rev Lett (2010)

Norm

aliz

ed

Direct gap (plusmnK)

Indirectgap

Transition Metal Dichalcogenides (TMD MX2)

Monolayer Isolation (PNAS 2005)Photoluminescence (PRL 2010)Monolayer FET(NNano 2011)Valleytronics (NNano 2012)Superconductivity (Science 2012)Photodetectors (NNano 2013)Light Emitting Diodes (Science 2014)Piezoelectic (Nature 2014)Laser (Nature 2015)Thermolelectrics (2015)

Graphene

TMD

Honeycomb lattice with broken inversion symmetry

Graphene TMDs

Massless Dirac fermion at plusmnK Massive Dirac fermion at plusmnK

119867 =0 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 0 119867 =

Δ 2 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 minus Δ 2

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 2: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

SARPES M Sakano K Ishizaka (Tokyo) S Shin K Yaji (ISSP) K Miyamoto T Okuda (Hiroshima)

High magnetic field measurements Y Kohama M Tokunaga (ISSP)

Theory T Oka (Dresden) M S Bahramy (Tokyo) Y YanaseY Nakamura (Kyoto)

Acknowledgements

Univ Tokyo Iwasa group

1 Introduction 2D materials Valley degree of freedom in TMDs

2 Valleytronics Valley Hall effect Circularly polarized light source

3 Superconductivity with spin-valley locking Enhanced Hc2 by SOI

Contents

n2D (cmndash2)

109 1011 1013 1015107

semiconductorinsulator

Si MOS-FET

metal

Interface

(GaAsAlGaAs)He surface

2D Electron Systems

httpwww2warwickacukfacsciphysicscurrenthttpsenwikipediaorgwiki2DEGhttpphysorgnews2011-02-

microwave-photons-nul

Electrochemical

Interfaces

2D crystalInterfaces

(LAOSTO

FeSeSTO)

2D Electron Systems rarr 2D Materials

Scotch Tape

CVD

MBE electrolyte

Family of 2D crystalline systems

Eg ( eV )

TMD (MX2)

M Mo W Ta hellip

XS Se Te

72 eV

(indirect)

06~23 eV

depending on

of layers

~2 eV (monolayer)

~03 eV (bulk)

Black PhosphorusGraphene

0 eV

h-BN

Valleytronics

Valley as information carriers

Candidate materialsSiDiamondAlAsBigraphene

ChallengeSearch for valley selective external perturbation

Direct gap in monolayer MoS2

Bulk Monolayer

Splendiani et al Nano Lett (2010)

4-layer 2-layer

Cao et al Nat Comm (2012)

Mak et al Phys Rev Lett (2010)

Norm

aliz

ed

Direct gap (plusmnK)

Indirectgap

Transition Metal Dichalcogenides (TMD MX2)

Monolayer Isolation (PNAS 2005)Photoluminescence (PRL 2010)Monolayer FET(NNano 2011)Valleytronics (NNano 2012)Superconductivity (Science 2012)Photodetectors (NNano 2013)Light Emitting Diodes (Science 2014)Piezoelectic (Nature 2014)Laser (Nature 2015)Thermolelectrics (2015)

Graphene

TMD

Honeycomb lattice with broken inversion symmetry

Graphene TMDs

Massless Dirac fermion at plusmnK Massive Dirac fermion at plusmnK

119867 =0 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 0 119867 =

Δ 2 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 minus Δ 2

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 3: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

1 Introduction 2D materials Valley degree of freedom in TMDs

2 Valleytronics Valley Hall effect Circularly polarized light source

3 Superconductivity with spin-valley locking Enhanced Hc2 by SOI

Contents

n2D (cmndash2)

109 1011 1013 1015107

semiconductorinsulator

Si MOS-FET

metal

Interface

(GaAsAlGaAs)He surface

2D Electron Systems

httpwww2warwickacukfacsciphysicscurrenthttpsenwikipediaorgwiki2DEGhttpphysorgnews2011-02-

microwave-photons-nul

Electrochemical

Interfaces

2D crystalInterfaces

(LAOSTO

FeSeSTO)

2D Electron Systems rarr 2D Materials

Scotch Tape

CVD

MBE electrolyte

Family of 2D crystalline systems

Eg ( eV )

TMD (MX2)

M Mo W Ta hellip

XS Se Te

72 eV

(indirect)

06~23 eV

depending on

of layers

~2 eV (monolayer)

~03 eV (bulk)

Black PhosphorusGraphene

0 eV

h-BN

Valleytronics

Valley as information carriers

Candidate materialsSiDiamondAlAsBigraphene

ChallengeSearch for valley selective external perturbation

Direct gap in monolayer MoS2

Bulk Monolayer

Splendiani et al Nano Lett (2010)

4-layer 2-layer

Cao et al Nat Comm (2012)

Mak et al Phys Rev Lett (2010)

Norm

aliz

ed

Direct gap (plusmnK)

Indirectgap

Transition Metal Dichalcogenides (TMD MX2)

Monolayer Isolation (PNAS 2005)Photoluminescence (PRL 2010)Monolayer FET(NNano 2011)Valleytronics (NNano 2012)Superconductivity (Science 2012)Photodetectors (NNano 2013)Light Emitting Diodes (Science 2014)Piezoelectic (Nature 2014)Laser (Nature 2015)Thermolelectrics (2015)

Graphene

TMD

Honeycomb lattice with broken inversion symmetry

Graphene TMDs

Massless Dirac fermion at plusmnK Massive Dirac fermion at plusmnK

119867 =0 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 0 119867 =

Δ 2 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 minus Δ 2

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 4: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

n2D (cmndash2)

109 1011 1013 1015107

semiconductorinsulator

Si MOS-FET

metal

Interface

(GaAsAlGaAs)He surface

2D Electron Systems

httpwww2warwickacukfacsciphysicscurrenthttpsenwikipediaorgwiki2DEGhttpphysorgnews2011-02-

microwave-photons-nul

Electrochemical

Interfaces

2D crystalInterfaces

(LAOSTO

FeSeSTO)

2D Electron Systems rarr 2D Materials

Scotch Tape

CVD

MBE electrolyte

Family of 2D crystalline systems

Eg ( eV )

TMD (MX2)

M Mo W Ta hellip

XS Se Te

72 eV

(indirect)

06~23 eV

depending on

of layers

~2 eV (monolayer)

~03 eV (bulk)

Black PhosphorusGraphene

0 eV

h-BN

Valleytronics

Valley as information carriers

Candidate materialsSiDiamondAlAsBigraphene

ChallengeSearch for valley selective external perturbation

Direct gap in monolayer MoS2

Bulk Monolayer

Splendiani et al Nano Lett (2010)

4-layer 2-layer

Cao et al Nat Comm (2012)

Mak et al Phys Rev Lett (2010)

Norm

aliz

ed

Direct gap (plusmnK)

Indirectgap

Transition Metal Dichalcogenides (TMD MX2)

Monolayer Isolation (PNAS 2005)Photoluminescence (PRL 2010)Monolayer FET(NNano 2011)Valleytronics (NNano 2012)Superconductivity (Science 2012)Photodetectors (NNano 2013)Light Emitting Diodes (Science 2014)Piezoelectic (Nature 2014)Laser (Nature 2015)Thermolelectrics (2015)

Graphene

TMD

Honeycomb lattice with broken inversion symmetry

Graphene TMDs

Massless Dirac fermion at plusmnK Massive Dirac fermion at plusmnK

119867 =0 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 0 119867 =

Δ 2 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 minus Δ 2

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 5: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Electrochemical

Interfaces

2D crystalInterfaces

(LAOSTO

FeSeSTO)

2D Electron Systems rarr 2D Materials

Scotch Tape

CVD

MBE electrolyte

Family of 2D crystalline systems

Eg ( eV )

TMD (MX2)

M Mo W Ta hellip

XS Se Te

72 eV

(indirect)

06~23 eV

depending on

of layers

~2 eV (monolayer)

~03 eV (bulk)

Black PhosphorusGraphene

0 eV

h-BN

Valleytronics

Valley as information carriers

Candidate materialsSiDiamondAlAsBigraphene

ChallengeSearch for valley selective external perturbation

Direct gap in monolayer MoS2

Bulk Monolayer

Splendiani et al Nano Lett (2010)

4-layer 2-layer

Cao et al Nat Comm (2012)

Mak et al Phys Rev Lett (2010)

Norm

aliz

ed

Direct gap (plusmnK)

Indirectgap

Transition Metal Dichalcogenides (TMD MX2)

Monolayer Isolation (PNAS 2005)Photoluminescence (PRL 2010)Monolayer FET(NNano 2011)Valleytronics (NNano 2012)Superconductivity (Science 2012)Photodetectors (NNano 2013)Light Emitting Diodes (Science 2014)Piezoelectic (Nature 2014)Laser (Nature 2015)Thermolelectrics (2015)

Graphene

TMD

Honeycomb lattice with broken inversion symmetry

Graphene TMDs

Massless Dirac fermion at plusmnK Massive Dirac fermion at plusmnK

119867 =0 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 0 119867 =

Δ 2 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 minus Δ 2

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 6: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Family of 2D crystalline systems

Eg ( eV )

TMD (MX2)

M Mo W Ta hellip

XS Se Te

72 eV

(indirect)

06~23 eV

depending on

of layers

~2 eV (monolayer)

~03 eV (bulk)

Black PhosphorusGraphene

0 eV

h-BN

Valleytronics

Valley as information carriers

Candidate materialsSiDiamondAlAsBigraphene

ChallengeSearch for valley selective external perturbation

Direct gap in monolayer MoS2

Bulk Monolayer

Splendiani et al Nano Lett (2010)

4-layer 2-layer

Cao et al Nat Comm (2012)

Mak et al Phys Rev Lett (2010)

Norm

aliz

ed

Direct gap (plusmnK)

Indirectgap

Transition Metal Dichalcogenides (TMD MX2)

Monolayer Isolation (PNAS 2005)Photoluminescence (PRL 2010)Monolayer FET(NNano 2011)Valleytronics (NNano 2012)Superconductivity (Science 2012)Photodetectors (NNano 2013)Light Emitting Diodes (Science 2014)Piezoelectic (Nature 2014)Laser (Nature 2015)Thermolelectrics (2015)

Graphene

TMD

Honeycomb lattice with broken inversion symmetry

Graphene TMDs

Massless Dirac fermion at plusmnK Massive Dirac fermion at plusmnK

119867 =0 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 0 119867 =

Δ 2 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 minus Δ 2

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 7: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Valleytronics

Valley as information carriers

Candidate materialsSiDiamondAlAsBigraphene

ChallengeSearch for valley selective external perturbation

Direct gap in monolayer MoS2

Bulk Monolayer

Splendiani et al Nano Lett (2010)

4-layer 2-layer

Cao et al Nat Comm (2012)

Mak et al Phys Rev Lett (2010)

Norm

aliz

ed

Direct gap (plusmnK)

Indirectgap

Transition Metal Dichalcogenides (TMD MX2)

Monolayer Isolation (PNAS 2005)Photoluminescence (PRL 2010)Monolayer FET(NNano 2011)Valleytronics (NNano 2012)Superconductivity (Science 2012)Photodetectors (NNano 2013)Light Emitting Diodes (Science 2014)Piezoelectic (Nature 2014)Laser (Nature 2015)Thermolelectrics (2015)

Graphene

TMD

Honeycomb lattice with broken inversion symmetry

Graphene TMDs

Massless Dirac fermion at plusmnK Massive Dirac fermion at plusmnK

119867 =0 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 0 119867 =

Δ 2 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 minus Δ 2

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 8: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Direct gap in monolayer MoS2

Bulk Monolayer

Splendiani et al Nano Lett (2010)

4-layer 2-layer

Cao et al Nat Comm (2012)

Mak et al Phys Rev Lett (2010)

Norm

aliz

ed

Direct gap (plusmnK)

Indirectgap

Transition Metal Dichalcogenides (TMD MX2)

Monolayer Isolation (PNAS 2005)Photoluminescence (PRL 2010)Monolayer FET(NNano 2011)Valleytronics (NNano 2012)Superconductivity (Science 2012)Photodetectors (NNano 2013)Light Emitting Diodes (Science 2014)Piezoelectic (Nature 2014)Laser (Nature 2015)Thermolelectrics (2015)

Graphene

TMD

Honeycomb lattice with broken inversion symmetry

Graphene TMDs

Massless Dirac fermion at plusmnK Massive Dirac fermion at plusmnK

119867 =0 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 0 119867 =

Δ 2 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 minus Δ 2

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 9: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Transition Metal Dichalcogenides (TMD MX2)

Monolayer Isolation (PNAS 2005)Photoluminescence (PRL 2010)Monolayer FET(NNano 2011)Valleytronics (NNano 2012)Superconductivity (Science 2012)Photodetectors (NNano 2013)Light Emitting Diodes (Science 2014)Piezoelectic (Nature 2014)Laser (Nature 2015)Thermolelectrics (2015)

Graphene

TMD

Honeycomb lattice with broken inversion symmetry

Graphene TMDs

Massless Dirac fermion at plusmnK Massive Dirac fermion at plusmnK

119867 =0 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 0 119867 =

Δ 2 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 minus Δ 2

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 10: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Honeycomb lattice with broken inversion symmetry

Graphene TMDs

Massless Dirac fermion at plusmnK Massive Dirac fermion at plusmnK

119867 =0 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 0 119867 =

Δ 2 120574 120591119902119909 + 119894119902119910

120574 120591119902119909 minus 119894119902119910 minus Δ 2

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 11: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Valley dependent optical selection rules

119895119911 = 0119895119911 = 0

119895119911 = 1119895119911 = minus1

Large spin-orbit interaction

119895119911 = ∓1

2

119895119911 = plusmn1

2

119895119911 = 1 plusmn1

2119895119911 = minus1 ∓1

2

Schematic of effective magnetic field

Xiao et al Phys Rev Lett (2012)

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 12: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Circularly polarized Photoluminescence

Cao et al Nat Comm (2012)Zeng et al Nat Nano (2012)Mak et al Nat Nano (2012)Sallen et al Phys Rev B (2012)

WSe2 MoSe2 MoS2 WS2

PL 63 5 56 42

Excitation by circularly polarized laser

Selective detection of σplusmn component

120578 =119868+ minus 119868minus119868+ + 119868minus

s+

s-

s- excitation

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 13: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Spin-valley locking

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry Spin-resolved ARPES

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 14: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

1ML MoS2 (P6m2)

MoS

Noncentro-

symmetric

K Krsquo

2H-MoS2 (P63 mmc)

Centro-

symmetric

6-fold

K Krsquo

S

3-fold

Bulk 3R-MoS2(R3m)

Noncentrosymmetric

Spin-Valley

coupling in bulk

3-fold

Monolayer vs Bulk

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 15: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Spin-valley locking

R Suzuki et al Nat Nano 9 611 (2014)

Spin-resolved ARPES

D Xiao et al PRL 108 196802 (2012)

Eint

Beff

Spin-Orbit Interaction

p

Broken inversion symmetry

P Kingrsquos group Nat Phys 10 385 (2014)

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 16: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Progress of valleytronics in monolayer TMDs

bull Circular dichroic PLH Zeng et al Nat Nano 7 490 (2012)

K F Mak et al Nat Nano 7 494 (2012)

T Cao et al Nat Comm 3 887 (2012)

bull EO conversion(valley light emitting transistor)Y J Zhang et al Science 344 725 (2014)

bull OE conversion(valley Hall effect)K F Mak et al Science 344 1489 (2014) J Lee et al Nat Nano 11 421 (2016)

bull Magneto-optics (valley Zeeman effect)

L Li et al PRL 113 266804 (2014)

D MacNeil et al PRL 114 037401 (2015)

A Srivastava et al Nat Phys 11 141 (2015)

G Aivasian et al Nat Phys 11 148 (2015)

120648+120648minus

-K K

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 17: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

wave vector

Bloch function

Berry curvature in monolayer MoS2

T Cao et al Nat Comm 2 887 (2012)

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 18: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

18

Hall effect

By external magnetic fields

Externalmagneticfield

Spontaneous Hall effect

Internalmagnetic

field

WIthout ernal magnetic fields

Hall effect

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 19: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

19

spin

magnon

phononelectron hole

valley

excitonoptical response

composite particles

Hall effect of excitons

1 ( ) 1( ) ( )

E

kr r Ω k

k

Anomalous velocity

Berry curvature

Potential gradienteg electric fields E

internal magnetic field

ldquoExciton with finite Berry curvaturerdquo

Valley excitons in TMDsCandidate

Various Hall effect Theory

W Yao et al Phys Rev Lett 101 106401 (2008)S I Kuga et al Phys Rev B 78 205201 (2008)

Spontaneous Hall effect

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 20: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 21: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Valley Hall effect in monolayer MoS2

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

Electrical detection of the optically excited

electrons and holes

σ

σ

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 22: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Valley Hall effect in monolayer MoS2

J Lee K F Mak et al Nature Nano 11 421 (2016)

Detection of the accumulated spins at the edge by Kerr rotation

Carrier doping by back gating

1 ( ) 1( ) ( )

E

kr r Ω k

k

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 23: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

K F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

S Konabe et al

PRB 90 075430 (2014)

Theory of

valley-Nernst effect

Valley Hall Effect in TMD monolayer

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 24: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Exciton Hall effectK F Mak et al

Science 344 1489 (2014)

J Lee et al

Nature Nano 11 421 (2016)

Berry curvaturePotential gradienteg electric fields E effective magnetic field

1 ( ) 1( ) ( )

E

kr r Ω k

k

Valley Hall Effect in TMD monolayer

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 25: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

25

Mo

S

Z Y Zhu et al PRB 84 153402 (2011)

Egap

excitonicstates

Absorption spectrum

200 meV

K F Mak et al Nat Mat 12 207 (2013)

stable excitons

Exciton in monolayer TMDs

two-dimensionality direct gap semiconductor

Transition metal dichalcogenides

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 26: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

PL mapping in monolayer MoS2

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 27: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

1 mm

Observation of exciton Hall effect

Polarization-resolved PL mapping(Pumped by linearly polarized light)

(under B = 0 )

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 28: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

I I Is s

(under B = 0 )-3 3

Polarization-resolved PL mapping(Pumped by linearly polarized light)

Observation of exciton Hall effect

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 29: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Color mapping of I

Hall effect of excitons visible objects

Tracing trajectories

1

-1

0

Conventional Hall effect

h e-

Trajectories of Hall effect

M Onga et al Nature Materials 16 1193 (2017)

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 30: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Definition amp evaluation

xxL

xyL3

Valley Hall Effect 10 cf

K F Mak et al Science 344 1489 (2014)

EHE 020 002xy

xx

L

L  

Large Hall angle(rarr real space observation)

Sample dependence

1 2 3

EHE 020 019 024

Internal structure of composite particles likely result in the large and non-trivial Berry curvature (due to exchange interaction)

H Yu et al Nat Comm 5 3876 (2014)

Hall angle of exciton hall effect

Trion

Exciton Due to the Bose nature of exciton the valley conductivity can be orders of magnitude larger than the Fermi one

T Yu and M W Wu PRB 93 045414 (2016)

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 31: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

107 109 1011 1013 1015105

Semiconductor MetalElectronic phase transitions

FET Electric Double Layer Transistor (EDLT)

Insulator

FET and EDLT (Electric Double Layer Transistor)

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 32: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

TMD-EDLT

FET vs EDLT (WSe2)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-100 -50 0 50 100

VG (V)

FET

EDLT

Carrier density (WSe2)

220K

15

12

9

6

3

0

n2

D (

x1

01

3

cm

2)

-4 -3 -2 -1 0 1 2

VG (V)

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2

10-11

10-10

10-9

10-8

10-7

10-6

10-5

I DS (

A)

-4 -3 -2 -1 0 1 2

VG (V)

WSe2MoS2

SiO2 (Novoselov et al PNAS (2005))

HfO2 (Radsavljevic et al Nat Nano (2011))

EDL (Zhang et al Nano Lett (2012))

S D

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 33: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Field-induced p-i-n Junction

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

Output curve

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

20

15

10

05

00

V4

T (

V)

43210

VDS (V)

VG = 2 V

40

30

20

10

0

I DS (m

A)

43210VDS (V)

VG = 2 V Cool down here

S D

VVV

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 34: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

20

15

10

5

0

I DS (m

A)

3210-1-2-3

VDS (V)

220 K

150 K

Field-induced p-i-n Junction

RH2RH1

-500

0

500

R

H1 (

)

-6 -3 0 3 6

B (T)

500

0

-500

R

H2 (

)

-6 -3 0 3 6

B (T)

Hall effect measurement

22 times 1013cm2minus15 times 1013cm2

Output curve

Zhang et al Nano Lett (2013)

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 35: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Electroluminescence from WSe2

2V

3V

4V

5V

6V

Bias

24

18

12

6

0

EL

in

ten

sity (

au

)

151050

Bias current (mA)

100 K

Ab

so

rptio

nP

L in

ten

sity

EL

in

ten

sity

22201816

Photon energy (eV)

excitation233 eV

A-exciton

B-exciton

He et al PRL (2014)

100 K

RT

RT

5 μm

AuTi

Y J Zhang et al Science 344 725 (2014)

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 36: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Electroluminescence from WSe2

SiN gating Pospischil et al Nat Nano (2014)

hBN gating Ross et al Nat Nano (2014)

HfO2 gating Baugher et al Nat Nano (2014)

Simultaneous publications

Current-induced circularly

polarized EL

EL

in

ten

sity (

au

)

165155145

Photon energy (eV)

s-

s+

EDL gating

Y J Zhang et al Science (2014)

40 K

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 37: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Electronic structure of gated multilayer MoS2

z

Real space (SC state)

Quasi-monolayer SC

n(z)

M S Bahramy

E

+

+

+

+

+

T Brumme et al

Phys Rev B 91 155436 (2015)

Gated multilayer is a mimic of monolayer

H T Yuan et al Nat Phys (2013)

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 38: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Electrical Control of Circular Polarization

WSe2

170 K

Field-effect doping is reversible and tunable

Modulation of diode profile

Circularly polarized light

source showing electrical

controllability

Y J Zhang et al Science (2014)

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 39: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Circularly Polarized EL from MoSe2

M Onga et al APL (2016)

MoSe2170 K

EL

in

ten

sity (

au

)

160155150145

Photon energy (eV)

6 K

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 40: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Helical Light Generation

Yang et al Adv Mater (2013)

httpwwwpttruhr-uni-bochumde

Structure

Angular momentum selection rule

Helicity control needs spin

(External magnetic field)

Spin LED Valley LET

Helicity can be controlled by current

(External in-plane electric field)

Optical filter

Konishi et al PRL (2011)

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 41: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

J T Ye et al Science 338 1193 (2012)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

102

103

104

105

106

107

Rs (

)

100806040200

T (K)

VEDLT=0V

VEDLT=6V

Gate induced superconductivity in MoS2

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 42: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Newly emerging 2D superconductors

MBE(layer-by-layer growth)

Pb In single layer (1L)Nature Phys 6 104 (2010)PRL 107 207001 (2011)

FeSe-1LCPL 29 03742 (2012)

Heavy Fermion superlattice

CVD

Mo2C-1~2LNature Mat 14 1135 (2015)

Ionic gating(EDLT)

ZrNCl-quasi-1LNature Mat 9 1314 (2010)Science 350 409 (2015)

TMDCs-quasi-1LScience 338 1193 (2012)Sci Rep 5 12534 (2015)Nature Nano 11 339 (2016) Nature Phys 12 144 (2016)

mechanically-exfoliated(2D crystals)

BSCCO-1LNature Comm 5 5708 (2014)

NbSe2-1LNano Letter 15 4914 (2015)Nature Nanotech 10 765 (2015)

intercalated graphene

STO amp KTO

Cuprate (LSCO)

Nature Mat 7 855 (2008) Nature Nano 6 408 (2011)

Nature 472 458 (2011)

PNAS 112 11795 (2015)ACS Nano 10 2761 (2016)

Nature Phys 7 849 (2011)

Tl-Pb single layer (1L)PRL 115 147003 (2015)

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 43: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

2D superconductors

Y Saito et al Nature Reviews Materials 2 16094 (2016)

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 44: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

EDLT New platform of 2D superconductivity

Enhanced Hc2 by SOI

Saito Nat Phys (2016)

Nonreciprocal Supercurrent

WakatsukiSaito Sci Adv (2017)Qin Nat Comm (2017)

Quantum Phase TransitionSaito Science (2015)

Nat Comm (2018)

(weak pinning) (broken inversion symmetry)

(materials)SrTiO3 KTaO3 LSCO YBCO ZrNCl MoS2 MoSe2 TiSe2 FeSe hellip

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 45: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Noncentrosymmetric superconductors

122

2 P

c

orb

c

H

H

Parity mixture

Benchmark Enhanced Pauli limit P

cH 2

To observe Pauli limit Maki parameter

Rashba-type spin polarization

Heavy electron massReduced dimensions

Two ways

CePt3Si

CeRhSi3 CeIrSi3 UirLi2Pt3B Li2Pd3B

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 46: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Monolayer MoS2 a new class of noncentrosymmetric SC

2H-type structure

z

Trigonal structure with simple band structure with out-of-plane spin polarization

Quasi-monolayer SC

n(z)

E

+

+

+

+

+

DFT calculation~ 1 layerBrumme et al PRB 91 155436 (2015)

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 47: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

R-T Curves for H and H (MoS2)

H

H

qc

H

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 48: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

20

15

10

5

0

Bc2 (T

)

1005000

T (K)

dSC 14 nm

GL(0) 81 nm

Pauli limit

H

2102

2

02

)1()0(2

12)(

)1()0(2

)(

c

scGL

c

c

GL

c

TTd

TH

TTTH

(0 = h2e)

2D Tinkam model

H

+

+

+

Thickness of superconductivity in MoS2-EDLT

Cf EDA rarr monolayerT Brumme et al PRB91 155436 (2015)

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 49: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

High field measurement at ISSP Univ Tokyo on gated MoS2

Experiment

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

Y Saito et al Nature Physics 12 144 (2016)

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 50: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Zero-field Zeeman splitting in conduction band in gated MoS2

Zeeman splitting (EF) = 13 meV

M S Bahramy

s + f symmetryFFLO

Intervalley pairing

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 51: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Comparison with Theory for MoS2

Hc2 semiquantitatively explained by Zeeman type spin-valley locking

Experiment Theory (Pauli limit)

Rashba

Zeeman

conventional Pauli limit

H

2D GL (orbital limit)

Enhanced Pauli limit

M S BahramyY Nakamura and Y Yanase

Y Saito et al Nature Phys 12 144 (2016)J M Lu et al Science 350 1353 (2015) X Xi et al Nature Phys 12 139 (2016)

Further theoryIlic et al PRL 119 117001 (2017)

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI

Page 52: Valleytronic Properties in 2D materialswebpark1651.sakura.ne.jp/workshop2018/MPI-UBC-UT... · 2018-02-17 · Definition & evaluation L xx L xy 3 Valley Hall Effect 10 cf. K. F. Mak

Summary Valleytronic Properties of 2D materials

1 Introduction

2 Exciton Hall effect

3 Valley Light Emitting Transistor

4 2D superconductivity Enhanced Hc2 by SOI


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