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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Summary Valleytronic Properties of 2D materials
1 Introduction
2 Exciton Hall effect
3 Valley Light Emitting Transistor
4 2D superconductivity Enhanced Hc2 by SOI