Scanning Gate Microscopy of the

QSH edge states Markus König, Andrei Garcia, David Goldhaber-Gordon

Stanford University

Christoph Brüne, Hartmut Buhmann, Laurens Molenkamp Universität Würzburg

-2,0 -1,5 -1,0 -0,5 0,0102

103

104

105

106

107

G = 2 e2/h

G = 0.005 e2/h

Rxx

/ Ω

Vg / V

45 Å 80 Å

Demonstration of QSHE in HgTe quantum wells

Present experimental results

Transport based on edge states

-2.5 -2.0 -1.5 -1.0 -0.5 0.00

2

4

6

8

10

5

10

15

20

25

R14

,23 (k

Ω)

Vgate (V)

I (n

A)

LB 6.4 kΩ

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

Present experimental results (2)

inelastic scattering magnetic field

Conductance is suppressed by

-2,0 -1,5 -1,0 -0,5 0,0102

103

104

105

106

107

G = 2 e2/h

G = 0.005 e2/h

Rxx

/ Ω

Vg / V

45 Å ( 1 µm x 1 µm) 80 Å (20 µm x 13 µm) 80 Å ( 1 µm x 1 µm)

G = 0.25 e2/h

-0,10 -0,05 0,00 0,05 0,100,0

0,2

0,4

0,6

0,8

1,0

90° 75° 60° 45° 30° 15° 10° 5° 0° G

norm

B / T

α

B

mean free path ~ 1 μm field strength ~ 10 mT

Open questions

Edge states: spatial arrangement width (Zhou et al., PRL (2008))

Stability of QSH state: Scattering due to potential fluctuations Breaking time reversal symmetry in B-field

Scanning Gate Microscopy

M.A. Topinka et al., Nature 410, 183 (2001)

M. Jura et al., Nature Physics 3, 841 (2007)

Basic SGM principles

tip potential induces perturbation leads to backscattering

decrease of conductance can be detected ΔG = 0

ΔG = 0

ΔG < 0

Application to QSH states

tip acts like local top gate potential fluctuation within the QSH regime Fermi level locally in conduction (valence) band

potential fluctuation can cause backscattering backscattering decreases conductance (only scattering into counter-propagating state)

G = 2e2/(3h)

Tip-induced scattering

Scattering mechanisms: 2D reservoirs Kondo impurities

2D reservoirs scattering sets in at critical Vtip

G saturates at predictable value Kondo-like impurities

scattering depends on occupation of impurity transition to 2D island for large impurity

G = 2e2/h 

Spatial mapping

AFM as complementary technique low-T AFM: in-situ comparison of transport results to spatial properties room-T AFM: high resolution of edge profile

details of scattering might affect results

Kondo: range of interaction? 2D island: size critical lower spatial resolution

spatial extension of edge states

Detailed study of scattering

sensitivity to potential fluctuations

dominant mechanism?

compensate intrinsic fluctuations for larger samples: G0 < 2 e2/h remove single perturbation by suitable tip potential

QSH states in magnetic field

low B: no full suppression of G high B: reentrant QH state

-0,10 -0,05 0,00 0,05 0,100,0

0,2

0,4

0,6

0,8

1,0

90° 75° 60° 45° 30° 15° 10° 5° 0° G

norm

B / T

α

B

0 2 4 6 8

-30

-20

-10

0

10

20

30

B / T

Rxy

/ kΩ

0,5 1,0 1,5 2,0 2,5 3,00

5

10

15

20

25

30

35

40

R /

kΩ

B / T

Tracking the states in high B-field

different scattering mechanisms (B vs. Vtip) tip perturbation leads to further decrease of

conductance change in sensitivity to tip perturbation? clear connection of QSHE and re-entrant QHE

σxy = e²/h σxy = 0 σxy = 0

Magnetic perturbation

commercial MFM tips: several 10 mT homogeneous perpendicular field: significant suppression for B = 10 mT effect of local field comparable? spatial variation of B-field effect?

dependence on intrinsic potential fluctuations increased sensitivity

combination of magnetic and electric perturbation

Summary

Scanning Gate Microscopy useful for more detailed characterization of QSH states spatial mapping scattering mechanisms

2D islands Kondo impurities breaking time reversal symmetry

behavior in high magnetic fields