Quantum Matter in High Magnetic Fields · 2017. 12. 8. · Quantum Matter in High Magnetic Fields...

Quantum Matter in

High Magnetic Fields

Uli Zeitler

Semiconductors & Nanostructures

High Field Magnet Laboratory (HFML – EMFL)

Institute for Molecules and Materials (IMM)

Radboud University, Nijmegen, the Netherlands

北京大学量子材 Seminar PKU-ICQM, 16-Nov-2017

Quantum Matter in High Magnetic Fields PKU-ICQM Seminar 16/11/20167 Uli Zeitler

Contents

• Part I - Who are we

IMM@RU, HFML / FELIX

Research at HFML

• Part II – Low dimensional materials in high fields

Graphene et al. – 2D materials

Measuring Chirality

Ising superconductivity in MoS2 and WS2

Topological Matter


Radboud University

www..ru.nl/

21 000 students

5 000 staff

300 professors

7000 publications

Broad Research University

The Netherlands


Institute for Molecules and Materials

www..ru.nl/imm

Theme 1: Structure and Dynamics of Molecules

Theme 2: Chemistry and Spectroscopy of Complex Molecular Systems

Theme 3: Quantum Matter

• Interdisciplinary research institute: Chemistry & Physics

• Mission: Fundamental research to understand, design and control the functioning of molecules and materials

• Research Facilities


Facilites @ IMM

www..ru.nl/imm

The IMM exhibits a multitude of advanced spectroscopic tools that allow for a detailed characterisation of matter in the nano-domain. Many facilities support each other and are used both by in-house and external users.

High Field Magnet Laboratory (HFML)

FELIX Laboratory (Free infrared lasers)

SPiN labs (Scanning probe)

NMR Laboratory

Life Science Trace Gas Facility

Clean rooms and laser facilities

HFML & FELIX @ Radboud University

http://www.ru.nl/felix/ http://www.ru.nl/hfml/

Cutting-edge technology Pioneering science

Mission of HFML/FELIX

• Develop infrared and THz sources

• Generate the highest possible DC-field

• Advanced instrumentation

• Research

- Molecular physics

- Condensed matter

• User facility

> 150 projects p/a

> 250 users p/a

• Public outreach

• Innovation

Smart Materials

Graphene / 2D materials

(topological) spintronics

High-Tc superconductors

Energy / Sustainability

catalysis: water H2

thermo-electricity

photosynthesis

Discover Control Manipulate

Health

targeted drug delivery

biomarkers for diagnosis

new structures for pharmaceuticals

Pioneering science Innovation

HFML/FELIX – a unique combination on a worldwide scale

IR/THz-FEL Facilities

DC HIGH-FIELD Facilities

>150 projects p.a.

>250 visitors p.a. from 25 countries


HFML @ RU


High Field Labs (HFML Nijmegen, Grenoble, Tallahassee, Tsukuba):

Superconductors 20 T

DC Bitter magnets & hybrid 30-45 T

Pulsed magnets (0.001s) 50-100T

Field strengths: typical magnetic fields

Highest man made fields (0.000001 s) Explosive, destructive 1000T

Neutron stars in the cosmos 100 000 000T

Magnetic fields at home: loudspeakers 1T

The earth magnetic field 0.000 05 T

The ‘smallest magnetic field: brain pulses 0.000 000 01 T

fridge magnet sticker 0.05 … 0.1 T


How to make high DC magnetic fields?

Cold water in

Magnetic Field

0 Bmax

20 MW DC supply

Cu

rre

nt

Heat-

exchanger

Warm water out


38 T resistive magnet

Bitter design

Cu/Ag disk

Isolation

Cooling Holes

Tie rod

37.53 T magnet:

• 40 kA, 21 MW

• 165 liter/sec water

2 Magnet halls, 6 magnets with

laboratoratories on top

Cooling installation, 7MW real

time, 165 l/s 25 Bar

22 MW, 40 000 A DC current,

550 V, 5 ppm ripple


European Magnetic Field Laboratory

Static fields

HFML Nijmegen

LNCMI Grenoble

Pulsed fields

HLD Dresden

LNCMI Toulouse

HFMLHLD

LNCMI-T

LNCMI-G

High field research facilities


Global players in high magnetic fields

USA

Tallahassee (DC)

Los Alamos (pulsed)

Japan

Tsukuba (DC)

Tokyo (pulsed)

China

Hefei (DC)

Wuhan (pulsed)

Europe

Nijmegen (DC)

Grenoble (DC)

Toulouse (pulsed)

Dresden (pulsed)


Everything is magnetic

Magnetic fields change the state of all matter through Lorentz force and spin splitting

in a reversible manner. Thermodynamic parameter

1.3185 1.3190 1.3195 1.3200

21 T

PL

In

ten

sity

(ar

b.

un

its)

Photon energy (eV)

19 T

Strongly correlated

electron systems

Soft condesed matter

& nanomaterials

Semiconductors &

nanostrucures

Research in high magnetic fields

http://www.sciencemag.org/content/vol315/issue5817/images/large/315_1379_F1.jpeg

http://www.sciencemag.org/content/vol315/issue5817/images/large/315_1379_F1.jpeg


Correlated matter

• Phase diagrams

• Superconductivity

• Magnetism

• Strange metals

• …..

Nigel Hussey & Alix McCollam


Soft Matter

Courtesy of Prof. J. Valles, Brown University, USA

e.g: Paramecium Caudatum

Peter Christianen & Hans Engelkamp


Paramecium Caudatum

Courtesy of Prof. J. Valles, Brown University, USA

Field: 0 T Field: 25 T


Semiconductors & Nanostructures

Hermann J. Suderow,

Opening the gate on superconductivity, Science 350, 1316 (1215)

MoS2

graphene

e.g.: 2D materials and devices

Uli Zeitler & Steffen Wiedmann


STM @ 35 T

W. Tao et al., Rev. Sci. Instr. 88, 093706 (2017).

Landau levels on graphite


Quantum Matter in

High Magnetic Fields


E ˆ H

ˆ 2

1

1

2

N

i

i em

Ap ˆ H

ßB g Bσ ˆ 2

1 *

,

)( j

ji

ieeV rr

)( i

ipV r

kinetic

potential

Zeeman

Coulomb

quantum Hall effect

magnetism

superconductivity

........

everything

Laplace´s Demon of quantum mechanics

semiconductor:

most versatile system

to tune properties

The theory of everything


1e

ˆ 2

1

*

1

2

Nm

B

em i

i

Ap

totßB Bg Bσ ˆ 2

1 *

,

Bl

eV

Br

j

ji

iee0

2

4)( rr

)( i

ipV r

Landau quantization

integer QHE

• quantization of momentum

• Landau-level degeneracy

(no BS!)

• LL separation determined by band structure

disorder potential (tend to ignore)

Landau-level broadening

localization

(single-particle) spin

interaction

QH ferromagnetism

FQHE

2DES is high magnetic fields

heB / L n


Quantum Hall effect

I

2DES

B

Uxx

Uxy

I

2DES

B

I

2DES

B

Uxx

Uxy

sweep magnetic field

successively depopulate Landau levels

1/B-periodic oscillations in Rxx

quantized plateaus in Rxy = (h/ne2)

Rxx 0 in quantum Hall plateaus

Rxx (kW

)

0 2 4 6 8 10

0

10

20

30

B (T)

0

1

2

3

4

n=2

1

34

6R

xy

(kW

)

D(E)

EEF

• Landau-quantized 2DES

• Localization between LL


Graphene

• mono-atomic layer of carbon

• first truly 2D system

(that should not exist !!)

• unique electronique properties

(zero-gap semiconductor with

massless chiral Dirac fermions)

Monolayers and bilayers

of graphite on SIMOX are visible

under an optical microscope

Other truly 2D systems

Novoselov et al., PNAS 2005

Blake et al., APL 2007

http://www.grapheneindustries.com/pages/Products/SiO2/flake on 90nm, large.png

http://www.grapheneindustries.com/pages/Products/SiO2/flake on 90nm, large.png


Other 2D materials: Borophene – Phosphorene

Silicence – Germanene – Stanene

Mannix et al.,

Science 350, 1513 (2015)

2D boron on Ag (111)

2D Ge on Pt (111)

Li et al.,

Adv. Mater. 26, 4820 (2016)

2D Si on Ag (110)

Aufrey et al.,

APL 96, 183102 (2010)Zhou et al.,

Nat. Mater. 14, 1020 (2015)

2D Sn on Bi2Te3

2D Black phosphorous


Hexagonal boron nitirde

• Insulator

• (nearly) latticed-matched

to graphene

• Substrate for graphene

heterostructures

(Hofstadter’s butterfly) Now: Stacking by exfoliation

Future (?): Layer-by-layer growth


Transition metal dichalcogenides

• Van-der-Waals stacking

• Bi-atomic graphene

• Direct-gap semiconductors

• Optical applications

• Valleytronics

• Photovoltaics

MoS2, WS2, MoSe2, WSe2, MoTe2


VG (V)

SiO2

gate insulator

Si backgate

Au contactsgraphite

Novoselov et al.,

Science 2004, PNAS 2005-80 -40 0 40 80

0

2

4

6

holes electrons

260 K

4 K

conducting “without” any charge carriers !!!

r(kW

)

Field effect doping in a MOSFET

ed

AV

e

CV

e

Qn r0

W k 6.5 4 2e

h

Ambipolar field-effect transistor


Novoselov et al; Zhang et al, Nature 2005

n (1012 cm-2)

xy

(4e

2/h

)

rxx (kW

)

-2-4 40 2

5

10

0

1.5

-1.5

-2.5

-3.5

-0.5

2.5

3.5

0.5

12T )( 4

21

2

Nh

exy

of four-fold degenerate Landau levels

Half-integer quantum Hall effect

)(221

212

, NeBcEN

chirality

pseudospin locked

to momentum


Vg (V)

rxx(kW

)

-6

2

4

-60 -30 0 6030

xy (e

2/h)

0

10

20

30

-4

-2

0

29 T

300 KB

E

EF

previously only below 30 K !

K.S. Novoselov et al., Science 315, 1379 (2007)

Room Temperature QHE at 30 T

T 30at K 2300 2 2

01 eBcE

more than just gaps !!


1.02

1.00

0.983.02.5

n or p (1013 cm-2 )

Rxy

(h/2

e2)

300 K

45 T

Rxy quantized

within 0.1 %

With:

Z. Jiang,* Y. Zhang, H. L. Stormer,

G. Boebinger,* and P. Kim,

Columbia University, New York, USA

*National High Magnetic Field Laboratory,

45 T

Room Temperature QHE at 45 T

K.S. Novoselov et al., Science 315, 1379 (2007)


Other 2D systems: QHE in InSe

D.A. Bandurin et al.; Nature Nanotechnology 12, 223 (2017).

• 6L InSe on BN

• High mobility (104 cm2 V−1 s−1)

• Conventional QHE with

spin-split Landau levels

• New playground for

quantum-Hall physics

( m* = 0.14, g ≈ 2 )

• High-speed electronics !?


Measuring Chirality

In Graphene


Chiral electrons in graphene

Gr – BN – Gr tunneling diode

K and K’-valleys displaced

“no” tunneling

Slight angular mismatch (~1o)

J. R. Wallbank et al.; Science 355, 575 (2016)


Resonant tunneling

emittercollector

Resonant tunneling at finite bias


Lorentz boost in a magnetic field

B

d

B

Δp (a) (b)

B field provides extra parallel momentum

can bring two slightly displaced valleys into resonance

Δp = -e d×B


Angular dependent tunneling

J. R. Wallbank et al.; Science 355, 575 (2016)

Bp = 28 T T = 4.2 K

• 60o-preiodic pattern

resonances with six K-valleys

• Asymmetric pattern

chiral section

• ideally: only one chirality can tunnel

(real life: 30%)

need smaller misalignment

and/or higher fields


TMDC field effect

transistors


Motivation

Carrier density dependent material properties


Monolayer WS2 transistor

Two types of gating

• Ion gating

set n 1014 cm-2

• Solid gate (Si/SiO2)

fine tune

n 1012 .. 1013 cm-2

MoS2: J.M. Lu et al.; Science 355, 575 (2016)

WS2: J.M. Lu et al.; arXiv:1703.06369 [cond-mat.supr-con].

Jianting Ye


Sweeping through the dome

effective voltage defined by

- Ion gate (kV, colours)

- Solid gate ( 80 V)

Insulator – (quasi) metal –

superconductor –

(quasi) metal – insulator

transition driven by gating

{ Phase defined by R(T) }


R (T)

- dR/dT < 0: insulator

- dR/dT > 0: (quasi) metal

- R = 0: superconductor


Phase diagram

Insulator – (quasi) metal –

superconductor –

(quasi) metal – insulator

transition driven by gating

Also seen in

- Hall mobility

- Hall concentration


Re-entrant insulator

Low n

Single exponential

Thermal excitation

from impurty band

High n

Two exponentials


Re-entrant insulator

High n

- Electrons trapped in

Coulomb traps of poorly

screened cations

- Coulomb interaction splits

impurity band into two

branches


Where is the Field?

Superconductor in a high field – a bad idea !


Superconductor in a high magnetic field

B

(nearly) no measurable suppression

of TC in parallel magnetic field

Pauli limit: Bpauli = 1.86 Tc = 3 .. 5 T


Pauli limit

Cooper pair

BCS = 1.76 kB T

Zeeman z = g B B

Pauli limit: BCSZ 2

paramagnetic breaking

of Cooper pairs


Ising protection

Pauli limit violator

External B

Orthogonality between spin and B

protects superconductivity

from paramagnetism

See also: Xing et al., Nano Lett..17, 6802 (2017).

Bp 250 T


Topological

matter @ HFML


Topological Insulators

“Definition”:

A topological insulator, like an ordinary insulator, has a bulk energy gap

separating the highest occupied electronic band from the lowest empty band.

The surface (or edge in 2D) of a topological insulator, however, necessarily has

gapless states that are protected by time-reversal symmetry.

strong spin-orbit interaction leads to topological insulating

electronic phases (applications ranging from spintronics to

quantum computation)

Topological insulators can be understood within the framework

of the band theory of solids

What is necessary for a topological insulator ?

How can we understand a topological insulator ?


2D Tis – HgTe quantum wells

inverted bandstructurenormal bandstructure

4 6 8 10 12-75

-50

-25

0

25

50

H3

H2

H1

E1

E (

me

V)

dQW (nm)

normal inverted band structure

dc


Temperature driven transition

→ task: perform magneto-transport experiments at different

temperatures

TEMPERATURE ?

S. Wiedmann et al., PRB, 91, 205311 (2015)


Low-temperature magnetotransport

→ ‘quantum Spin Hall regime’ for

a quantum well with d=12 nm

Vg



Magnetotransport at 300 K

→ two-carrier charge transport at T=300 K


Temperature-driven transition


Eight-band k·p band structure calculations

dispersion


3D Ti – strained HgTe

Ambipolar surface QHE

top surface

bottom surface

0 5 10 15 20 25 300

5

10

15

20

Rxx (

kW

)

electrons

0

5

10

15

-4V

-6V

i=2

i=4i=3

Rxy (

kW

)

i=7+3V

0 5 10 15 20 25 300

10

20

30

i=6i=4

i=2i=7

i=5i=3

B (T)

holes

Rxx (

kW

)

-15

-10

-5

0

Rxy (

kW

)

0 5 10 15 20 25 300

10

20

30

40

i=1i=7

i=5i=3

holes

Rxx (

kW

)

-30

-20

-10

0

Rxy (

kW

)

4 2 0 -2 -4 -6-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

nbottom surface

ntop surface

nHall

nbottom surface

+ntop surface

n, p (

10

12 c

m-2)

Vg (V)

0 50 100 150 2000.3

0.4

0.5

0.6

0.7

Rxx (

kW

)

T (K)

Vg=0

• 3D bulk states

• Topological 2D surface states


Thermoelectric power in strained HgTe

Heater: ~500 Ω

Thermometers: RuOx - matched

heater thermometers

sample contacts

5 cm

cold sink

in vacuum

𝑆𝑥𝑥 =−𝐸𝑥𝛻𝑥𝑇

𝑆𝑥𝑦 =−𝐸𝑦

𝛻𝑥𝑇

Seebeck effect:

Nernst-Ettingshausen effect:

diffusion TEP / phonon drag

A. Jost et al., PNAS 114 , 3381 (2017)


Low-field data

63

Transition from electrons to holes

Dirac point of surface states

at Vg=-1.85 V

Vg> 0: electrons; Vg<0: holes

TEP constant for electrons

|Sxx,holes |~ 30·|Sxx,electrons|

Maximum in Sxy at Dirac point

Small maximum in Sxx at Dirac point

Diffusion TEP:

0

1

2

3

4

B = 0T

Rxx (

kW

)

T = 1.2K

B = 0.2T

T = 1.5K

B = 0T

-10

0

10

20

30

Sxx (

V/K

)

-4 -2 0 2

0

20

40

60

Sxx (

V/K

)

Vg (V)

T = 1.5K

B = 0.2T*

0.0

0.4

0.8

Rxy (

kW

)

15

20

25

30

35

S xy (

V/K

)


High-field quantum oscillations

0 4 8 120

100

200

i=-5

i=-3

B (T)

Sxx (

V/K

)

0

40

80

120

holes

i=4

-Sxx (

V/K

)

i=3electrons

0.0

0.2

0.4

0.6

0.8r

xx (

kW)

0.0

0.4

0.8

1.2

rxx

(kW

)

-> as in transport: odd sequence of plateaus is observed

0 4 8 12 160

200

400

600

7 56

4

7 5

4

7 53

7 5

-6.0V

-5.5V

-5.0V

S xx (

V/K

)B (T)

-4.5V3

nt

sn

b

s

DOS

E

top

bottom

top

bottom

nt

s=n

b

s

E

DOS


Conclusions

• High magnetic field as a probe to condensed matter

Semiconductors – metals – superconductors

and the new fundamental phenomena therein

Soft matter can also be fun

• 2D Materials - a rising star of condensed matter science

New physics in graphene et al.: QHE and more

Chirality can be controlled Chiralotronics

Extremely protected Ising superconductor WS2

High fields can reveal topological states in 2D and 3D

Apply for magnet time: http://www.emfl.eu/user.html

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