H. Buhmann H. Buhmann

H. Buhmann H. Buhmann

2d Dirac system

• hybridization of the top and bottom surface lead to a gapped

states on these two surfaces

• free 1d Dirac electrons at the edges of the layer

H. Buhmann H. Buhmann

2d to 3d transition

• hybridization of the top and

bottom surface is lifted

• gapless surface state are

recovered

H. Buhmann H. Buhmann

3d Dirac system

free 2d Dirac electrons on all six surfaces

H. Buhmann

Bi Compounds

H. Buhmann

Bi Compounds

H. Buhmann

Bi1-xSbx

Theory: Predict Bi1-xSbx is a topological insulator by exploiting

inversion symmetry of pure Bi, Sb (Fu,Kane PRL’07) Experiment: ARPES (Hsieh et al. Nature ’08)

• Bi1-x Sbx is a Strong Topological

Insulator 0;(1,2,3) = 1;(111)

• 5 surface state bands cross EF

between G and M

ARPES Experiment : Y. Xia et al., Nature Phys. (2009).

Band Theory : H. Zhang et. al, Nature Phys. (2009). Bi2 Se3

• 0;(1,2,3) = 1;(000) : Band inversion at G • Energy gap: D ~ .3 eV: A room temperature

topological insulator

• Simple surface state structure :

Similar to graphene, except

only a single Dirac point EF

3D Topological Insulator

H. Buhmann

Bi2Se3 242 with Se cap

Surface structure of Bi2Se3

Remaining of Se cap

Thickness of Bi2Se3 layer is about 100 nm

Surface Termination

H. Buhmann

Si surface

Bi2Se3

Additional QL

Growth Start

H. Buhmann

Dislocations

H. Buhmann H. Buhmann

Bi2Se3

pro

wide gap > 300 meV

(RT application possible!)

con

crystal quality?

low mobility (100 – 1000 cm2/(Vs))

very high unintentional doping

no clear transport signatures of

Dirac surface states

H. Buhmann H. Buhmann

H. Buhmann

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

-400

-300

-200

-100

0

100

EF

E, m

eV

k, nm-1

Bulk HgTe

fully strained

70 nm HgTe

on CdTe substrate

Band Structure

- gap openning (10…20 meV)

- two Dirac cones on

different surfaces

L1

H1

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

dga

p e

ner

gy

(eV

)

lattice constant a [Å]0© CT-CREW 1999

E1

H. Buhmann

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

-400

-300

-200

-100

0

100

EF

E, m

eV

k, nm-1

Bulk HgTe

x-ray diffraction (115 reflex)

fully strained

70 nm HgTe

on CdTe substrate

Band Structure

- gap openning (10…20 meV)

- two Dirac cones on

different surfaces

L1

H1

E1

H. Buhmann

Bulk HgTe

B

I

Hall effect measurement

H. Buhmann

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)

Rxx in O

hm

B in Tesla

n=4

n=3

Rxy

(Hall)

Rxy in O

hm

n=2

QHE in a 3D TI system

H. Buhmann

2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

s

xy [e

2/h

]

B [T]

0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

0

2

4

6

8

10

12

14

Rxx [k

]

B [T]

Rxy [k

]

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

QHE in a 3D TI system

h

enxy

2

2

1

s

single Dirac

surface

H. Buhmann

2 4 6 8 10 12 14 160

2000

4000

6000

8000

10000

Rxx in

Oh

m

B in Tesla

DO

S

Density of states for two independent surfaces with slightly different density

2-11

2

-211

1

cm 1085.4

cm 107.3

n

n

QHE in a 3D TI system

B

I

H. Buhmann

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

QHE in a 3D TI system

H. Buhmann

QHE in a 3D TI system

0 2 4 6 8 10 12 14 16

-1

0

1

2

3

4

5 0

5

10

15

20

25

Vgate [V

]

B [T]

Rx

y [

k

]

Rxy from -1 V to 5 V n = 1

n = 3

n = 5

flat band condition at -1 V top and bottom surface exhibit approx. the same

carrier density.

h

enxy

2

12 s for ntop = nbottom

H. Buhmann

0 2 4 6 8 10 12 14 16

-1

0

1

2

3

4

5 0

5

10

15

20

25

Vgate [V

]

B [T]

Rx

y [

k

]

QHE in a 3D TI system Rxy and Rxx from -1 V to 5 V

0 2 4 6 8 10 12 14 16

-1

0

1

2

3

4

5 0

10

20

30

40

Vgate [T

]

B [T]

Rx

x [

k

]

0 5 10 15

-20

-10

0

10

20

30

n=3.2*1011

cm-2

E, m

eV

B, T

0.00 0.05 0.10 0.15 0.20 0.25

-150

-100

-50

0

50

n=3.2*1011

cm-2

E, m

eV

k, nm-1

Band structure and Landau level at the symmetry point

H. Buhmann

QHE in a 3D TI system

0 5 10 15

-20

-10

0

10

20

30

n=3.2*1011

cm-2

E, m

eV

B, T

0.00 0.05 0.10 0.15 0.20 0.25

-150

-100

-50

0

50

n=3.2*1011

cm-2

E, m

eV

k, nm-1

Band structure and Landau level at the symmetry point

20 40 60 80 100

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

6.3

5.45

3.6

2

0

|(k

F)|

2

n, 10

11 c

m-2

z, nm

development of the top and bottom

surface state

H. Buhmann H. Buhmann

Parameters devices A and B (similar design) HgTe: Thickness mesa: D 70 nm (structure etched 108 nm deep) Dimensions junction: L x W L x 2000 nm with LA 1000 nm LB,C 350 nm LD,E,F 150 nm

HgTe

E F

devices

L W

D C B A

Nb: Thickness: d 68 nm Width: w 500 nm Length: l 2000 nm (crossing the complete width of the HgTe mesa)

Capping layer: 10 nm Al and 10 nm Ru

Nb Nb Nb Nb Nb Nb Nb Nb

G

H. Buhmann

Summary

observation in 2D systems

– quantum spin Hall effect

• spin polarized quantized edge channel transport

observation in 3D systems

– quantum Hall effect of two Dirac surfaces

– proximity induced super conductivity

H. Buhmann

Acknowledgements

Quantum Transport Group (Würzburg, H. Buhmann)

C. Brüne

C. Ames

P. Leubner

L. Maier

M. Mühlbauer

C. Thienel

J. Mutterer

D. Knott

A. Astakhova

Ex-QT: C.R. Becker

T. Beringer

M. Lebrecht

J. Schneider

S. Wiedmann

N. Eikenberg

R. Rommel

F. Gerhard

B. Krefft

A. Roth

B. Büttner

R. Pfeuffer

R. Schaller

Stanford University

S.-C. Zhang

X.L. Qi

(J. Maciejko)

(T. L. Hughes)

M. König

Texas A&M University

J. Sinova

Lehrstuhl für Experimentelle Physik 3: L.W. Molenkamp

Univ. Würzburg

Inst. f. Theoretische Physik

E.M. Hankiewicz

B. Trautzettel

Collaborations:

Penn. State University

CX. Liu

H. Buhmann H. Buhmann

Quantum Spin Hall Effekt

Science 318, 766 (2007)

The Quantum Spin Hall Effect:

Theory and Experiment

J. Phys. Soc. Jap.

Vol. 77, 31007 (2008) Intrinsic Spin Hall Effekt

Nature Physics 6, 448 (2010)

Nonlocal edge state transport

in the quantum spin Hall state

Science 325, 294 (2009)

Quantum Hall Effect from the

Topological Surface States of

Strained Bulk HgTe

Phys. Rev. Lett. 106, 126803 (2011)

Spin polarization of the quantum

spin Hall edge states

Nature Physics, 8,485 (2012)