Laurens W. Molenkamp

Physikalisches Institut, EP3Universität Würzburg

Overview

- HgTe/CdTe bandstructure, quantum spin Hall effect- Dirac surface states of strained bulk HgTe- Josephson junctions and SQUIDs

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.76.6

1.0

1.5

0.5

0.0

-0.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

6.0

5.5

Bandgap vs. lattice constant(at room temperature in zinc blende structure)

Ban

dgap

ene

rgy

(eV

)

lattice constant a [Å]0 © CT-CREW 1999

MBE-Growth

HgTe-Quantum Wells

band structure

D.J. Chadi et al. PRB, 3058 (1972)

fundamental energy gap

meV 30086 EE meV 30086 EE

semi-metal or semiconductor

HgTe

-1.0 -0.5 0.0 0.5 1.0k (0.01 )

-1500

-1000

-500

0

500

1000

E(m

eV) 8

6

7

-1.0 -0.5 0.0 0.5 1.0k (0.01 )

-1500

-1000

-500

0

500

1000

E(m

eV) 8

6

7

Eg

-1.0 -0.5 0.0 0.5 1.0k (0.01 )

-1500

-1000

-500

0

500

1000

E(m

eV)

HgTe

8

6

7

-1.0 -0.5 0.0 0.5 1.0k (0.01 )

Hg0.32Cd0.68Te

-1500

-1000

-500

0

500

1000

E(m

eV)

6

8

7

VBO

-1.0 -0.5 0.0 0.5 1.0k (0.01 )

-1500

-1000

-500

0

500

1000

E(m

eV)

HgTe

8

6

7

-1.0 -0.5 0.0 0.5 1.0k (0.01 )

Hg0.32Cd0.68Te

-1500

-1000

-500

0

500

1000

E(m

eV)

6

8

7

VBO

BarrierQW

VBO = 570 meV

HgTe-Quantum Wells

Layer Structure

gate

insulator

cap layer

doping layer

barrier

barrierquantum well

doping layer

buffer

substrate

Au

100 nm Si N /SiO

3 4 2

25 nm CdTe

CdZnTe(001)

25 nm CdTe10 nm HgCdTe x = 0.79 nm HgCdTe with I10 nm HgCdTe x = 0.74 - 12 nm HgTe10 nm HgCdTe x = 0.7 9 nm HgCdTe with I10 nm HgCdTe x = 0.7

symmetric or asymmetricdoping

Carrier densities: ns = 1x1011 ... 2x1012 cm-2

Carrier mobilities: = 1x105 ... 1.5x106 cm2/Vs

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 80

100

200

300

400

500

µ=1.06*106cm2(Vs)-1

nHall=4.01*1011cm-2

Q2134a_Gate

B[T]

Rxx

[]

-15000

-10000

-5000

0

5000

10000

15000

Graph2

Rxy

[]

Type-III QW

VBO = 570 meV

HgCdTeHgCdTeHgTe

HgCdTe

HH1E1

QW < 63 Å

HgTe

inverted normal

band structure

conduction band

valence band

HgTe-Quantum Wells

123456

k (0.01 -1)

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Ener

gyE(

k)(e

V)

k || (1,1)k || (1,0)k = (kx,ky)

k || (1,1)k || (1,0)k = (kx,ky)

4 nm QW 15 nm QW

normal

semiconductor

inverted

semiconductor

1 2 3 4 5 6

k (0.01 -1)

-0.20

-0.15

-0.10

-0.05

0.00

0.50

0.10

0.15

0.20

E2

H1H2

E1L1

0.6 0.8 1.0 1.2 1.4

dHgTe (100 )

E2E2

E1E1H1H1

H2H2H3H3

H4H4 H5H5

H6H6L1L1

Band Gap Engineering

A. Pfeuffer-Jeschke, Ph.D. Thesis, Würzburg University (2000)

Bandstructure HgTe

E

k

E1

H1

invertedgap

4.0nm 6.2 nm 7.0 nm

normalgap

H1

E1

B.A Bernevig, T.L. Hughes, S.C. Zhang, Science 314, 1757 (2006)

Topological Quantization

C.L.Kane and E.J. Mele, Science 314, 1692 (2006)

C.L.Kane and E.J.Mele, PRL 95, 146802 (2005)C.L.Kane and E.J.Mele, PRL 95, 226801 (2005)A.Bernevig and S.-C. Zhang, PRL 96, 106802 (2006)

QSHE, Simplified Picture

normalinsulator

bulk

bulkinsulating

entire sampleinsulating

m > 0 m < 0

QSHE

Experimental Signature

normal insulator state

QSHI

Observation of QSHI state

M. König et al., Science 318, 766 (2007).

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0103

104

105

106

G = 2 e2/h

Rxx

/

(VGate- Vthr) / V

Observation of QSH Effect

(1 x 0.5) m2

(1 x 1) m2(2 x 1) m2

(1 x 1) m2

non-inverted

1 m 2 m

1 2 3

6 5 4

1 m

1 m

5 m

1 2

34

(a) (b)

Verify helical edge state transport

Multiterminal /Non-local transport samples

Multi-Terminal Probe

210001121000012100001210000121100012

T

heIG

heIG

t

t

2

23

144

2

14

142

232

generally

22 2)1(

ehnR t

3exp4

2 t

t

RR

heG t

2

exp,4 2

Landauer-Büttiker Formalism normal conducting contacts no QSHE

0.0 0.5 1.0 1.5 2.00

5

10

15

20

25

R (k

)

V* (V)

I: 1-4V: 2-3

1

3

2

4

R14,23=1/4 h/e2

R14,14=3/4 h/e2

Non-Local data on H-bar

A. Roth et al., Science 325, 294 (2009).

Configurations would be equivalent in quantum adiabatic regime

-1 0 1 2 30

5

10

15

20

25

30

35

40

R (k

)

V* (V)

I: 1-4V: 2-3

R14,23=1/2 h/e2

R14,14=3/2 h/e2

I: 1-3V: 5-6

R13,13=4/3 h/e2

R13,56=1/3 h/e2

-1 0 1 2 3 4

V* (V)

Multi-Terminal Measurements

A. Roth et al., Science 325, 294 (2009).

QSHE and iSHE as spin injector and detector

Split-gated H-bar

Detect iSHE through QSHI edge channels

I

U

Gate in 3-8 leg is scanned, 2-9 leg is n-type metallic,

current passed between contacts 2 and 9.

C. Brüne et al., Nature Physics 8, 486–491 (2012)

Detect QSHI throughinverse iSHE

I

U

Gate in 3-8 leg is scanned, 2-9 leg is n-type metallic,

current passed between contacts 3 and 8 C. Brüne et al., Nature Physics 8, 486–491 (2012).

Scanning SQUID

K.C. Nowack et al., Nature Materials 12, 787 (2013).(with Kam Moler group, Stanford)

Bulk HgTe as a 3-D Topological ‚Insulator‘

-1.0 -0.5 0.0 0.5 1.0k (0.01 )

-1500

-1000

-500

0

500

1000

E(m

eV) 8

6

7

-1.0 -0.5 0.0 0.5 1.0k (0.01 )

-1500

-1000

-500

0

500

1000

E(m

eV) 8

6

7

Bulk HgTe is semimetal,

topological surface state overlaps w/ valenceband.

k(1/a)

E-E

F(eV

)

ARPES: Yulin Chen, ZX Shen,

StanfordC. Brüne et al., Phys. Rev. Lett. 106, 126803 (2011).

70 nm layer on CdTe substrate:coherent strain opens gap

0 2 4 6 8 10 12 14 160

2000

4000

6000

8000

10000

12000

14000

16000

0

2000

4000

6000

8000

10000

12000

14000

Rxx (SdH)

R

xx in

Ohm

B in Tesla

Rxy (Hall)

Rxy

in O

hm

Bulk HgTe as a 3-D Topological ‚Insulator‘

@ 20 mK: bulk conductivity almost frozen out - Surface state mobility ca. 35000 cm2/Vs

C. Brüne et al., Phys. Rev. Lett. 106, 126803 (2011).

3D HgTe-calculations

2 4 6 8 10 12 14 160

2000

4000

6000

8000

10000

2.73.54.45.67.69.711 33.94.96.78.510.112

experiment

Rxx

in O

hm

B in Tesla

n=3.7*1011 cm-2

n=4.85*1011 cm-2

n=(4.85+3.7)*1011 cm-2

DO

S

Red and blue lines : DOS for each of the Dirac-cones with the corresponding fixed 2D-density,Green line: the sum of the blue and red lines

C. Brüne et al., Phys. Rev. Lett. 106, 126803 (2011).

Experiments on a gatedHallbar

0 2 4 6 8 10 12 14 16

-10

12

34

5 0

5

10

15

20

25

Vgate [V]

B [T]

Rxy

[k

]

Rxy from -1.5V to 5V

C. Brüne et al., Phys. Rev. X 4, 041045 (2014).

0 2 4 6 8 10 12 14 16-3-2-1012345

7 3

5

6

5

4

3

2

V g [V]

B [T]

n=1

Two distinct Landau fans

Different gate efficiency, large dielectric constant. Note the absence of spin splitting.

C. Brüne et al., Phys. Rev. X 4, 041045 (2014).

Different mobilitiesfor top and botttom

C. Brüne et al., Phys. Rev. X 4, 041045 (2014).

More plots

Constant (small) deviation Berry phase for Dirac fermions

Transport exclusively through surface states, for all gate voltages.Cause: Dirac systems have different screening properties from parabolic bands,resulting in a smaller dielectric constant(cf. E.H. Wang, S. das Sarma, Phys. Rev B 75, 205418 (2007), D. DiVincenzo, G. Mele, Phys. Rev B 29, 1685 (1984).

Sample "Quad", device ADevice with improved HgTe-Nb interfaces.

Nb Nb

CdTe

70 nm strained HgTe

I

V

W=

2 m

stra

ined

HgT

e

Nb Nb

L = 1000 nm

D=

200

nm

V

I

J. Oostinga et al., Phys. Rev. X 3, 021007 (2013).

Supercurrent regimeAt T = 25 mK, 200 mK, 500, 800 mK

-6 -4 -2 0 2 4 6

x 10-6

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

x 10-4 I-V at different temperatures

I / A

Usa

mpl

e / V

800 mK500 mK200 mK

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

x 10-5

-5

-4

-3

-2

-1

0

1

2

3

4

5x 10-4 I - V at B = 0 mT, T = 25 mK

I / A

Usa

mpl

e / V

20120411_004 (<-)20120412_001 (<-)20120412_002 (->)

sI

sIrI

rI

Switching current depends on sweeping direction (origin unknown):

Retrapping current does not depend on sweeping direction:

ss II rr II

IcRN 0.15-0.2 mV

At T = 25 mK:Ic Is 3-4 A

RN 50

T 25 mKJust DC

Could of course just be inhomogeneouscurrent injection.

Need otherexperiments toidentify exoticsuperconductivity.

J. Oostinga et al., Phys. Rev. X 3, 021007 (2013).

Sample with two contacts shows somewhat irregular ‚Fraunhofer‘ pattern.

AC SQUIDs

Scanning SQUID: Ilya Sochnikov(with Kam Moler group, Stanford)

0 500 10000

0.2

0.4

0.6

0.8

1

0 500 10000

0.05

0.1

0.15

0.2

0.25

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

-1

-0.5

0

0.5

1

I (μA

)

Applied flux (Φ0)

Applied flux (Φ0)

I/Ic

(a)

(b)

L = 200 – 600 nm

Nb

HgTe

Asy

mm

etry

Junctions length (μm)Junctions length (μm)

I c(μ

A)

(c) (d)

200 nm300 nm400 nm500 nm600 nm

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

-1

-0.5

0

0.5

1

200 nm300 nm400 nm500 nm600 nm

Clearly non-sinusoidal I- curve

Ballistic junction?Exotic superconductivity? .

T=450 mK

I. Sochnikov et al., Phys. Rev. Lett. 114, 066801 (2015).

Contacting the edge channelsin quantum wells

S. Hart et al., Nature Physics 10, 638–643 (2014).(with Amir Yacoby & group, Harvard)

Gate induces QSH regime,infer current distribution fromFraunhofer pattern.

Conclusions– HgTe quantum wells: normal and inverted gap, linear (Dirac) dispersion

– show Quantum Spin Hall Effect

– demonstrated helical edge channels and spin polarization

– strained 3D layers show QHE of topological surface states

– In which a - very peculiar - supercurrent can be induced

Collaborators:Erwann Bocquillon, Christoph Brüne, Hartmut Buhmann, Markus König, Luis Maier, Matthias Mühlbauer, Jeroen Oostinga, Cornelius Thienel….Teun Klapwijk, David Goldhaber-Gordon, Kam Moler, Amir Yacoby, Andrei Pimenov, Marek Potemski, Seigo TaruchaTheory: Alena Novik, Ewelina Hankiewicz , Grigory Tkachov, BjörnTrauzettel (all @ Würzburg), Jairo Sinova (Mainz), Shoucheng Zhang, Xiaoliang Qi (Stanford), Chaoxing Liu (Penn State)

Funding: DFG (SPP Topological Insulators, DFG-JST FG Topotronics, Leibniz project), Humboldt Stiftung, EU-ERC AG “3-TOP”, DARPA