Imaging transmission of nanostructures in a high-mobility heterostructure

Aleksey KozikovClemens RösslerThomas IhnKlaus Ensslin

C. ReichlW. Wegscheider

Local electron transport

• Diffusive/ballistic transport

• Classical/quantum phenomena

Motivation

Ultra high-mobility:

• lp >> L Ballistic transport: electron trajectories are straight lines

• Modulation doping technique Small-angle scattering:

electron trajectories are wavy lines

How does small-angle scattering affect transport?

Motivation

QPC

2DEG

x

y

Conductance, G

M. Topinka et al. Nature 410, 183-186 (2001)

Motivation

300 K115 K0.24 K

Local relocation of charge between donor sites

Scannell et al. PRB 85, 195319 (2012)

Motivation

Wilkinson et al. Nature 380, 608 (1996)

Conductance through a tunneling diode

MotivationExperimental data Filtered data

Crook et al. PRL 91, 246803 (2003)

MotivationExperimental data TheoryFiltered data

No one-to-one correspondenceAoki et al. PRL 108, 136804 (2012)

Sample

n = 1.2 × 1015 m-2

EF = 4 meVλF = 72 nmµ = 850 m2/Vslp = 49 µmDStadium = 3 µm

Excellent wafers:C. ReichlW. WegscheiderETH Zurich

Golden top gates

QPC Ballisticstadium

2DEG 1 µm

Quantum point contact

Top gates

2DEG

Electron flowD. A. Wharam et al., 1988B. J. van Wees et al., 1988

-0.8 -0.6 -0.40

2

4

6

Con

duct

ance

, (2

e2 /h)

Gate voltage, (V)

EF

Energy TipTop gates

2DEG

SGM technique

Backscattering effect

n

nTh

eG

22

Landauer-Büttiker theory of transport

d

D. A. Wharam et al., 1988B. J. van Wees et al., 1988

-0.8 -0.6 -0.40

2

4

6

Con

duct

ance

, (2

e2 /h)

Gate voltage, (V)

Electron backscattering through the QPC

3rd plateau

Vtip= -6.0 Vd = 70 nm

1 µm

xy

Differential conductance, dG/dx

arXiv:1206.1371

• Gate voltage dependence• Tip voltage dependence• Tip-surface distance dependence• Temperature dependence• Source-drain bias dependence• QPC asymmetry dependence• Magnetic field dependence: backscattering is

essential

o Strongly varying interference fringe spacing (50%)

0.5 µm

X (µm)

y (µ

m)

Scanning gate microscopy on a QPC

arXiv:1206.1371Small-angle scattering

Vtip= -8.0 V

Vstadium= -0.5 V

Scanning gate microscopy on a stadiumdG/dx

X (µm)

1 µmy

(µm

)

Scanning gate microscopy on a stadiumdG/dx

Vtip= -8.0 V

Vstadium= -0.8 V

X (µm)

1 µmy

(µm

)

Scanning gate microscopy on a stadiumdG/dx

Vtip= -8.0 V

Vstadium= -2.0 V

X (µm)

1 µmy

(µm

)

Vtip= -8.0 V Vstadium= -0.8 V

Scanning gate microscopy on a stadiumG (2e2/h)dG/dx

1 µm 1 µm

500 nm

Scanning gate microscopy on a stadiumdG/dx

Scanning gate microscopy on a stadium

dG/dx

G (2e2/h)dG/dx

a

b

c

d

Qualitative model

a

b

c

d

𝐺𝑇𝑜𝑡𝑎𝑙=1/𝑅𝑇𝑜𝑡𝑎𝑙

Qualitative model

𝑅  𝑇𝑜𝑡𝑎𝑙=𝑅  𝑎∨¿𝑅  𝑏+𝑅  𝑐+𝑅  𝑑+𝑅  𝑐𝑟

𝑅  𝑇𝑜𝑡𝑎𝑙=(𝑒2

h𝑎+

𝑒2

h𝑏)

−1

+(𝑒2

h𝑐)

−1

+¿

+(𝑒2

h𝑑)

− 1

+𝑅𝑐𝑟

contact resistance

Rcr

Assumptions: Rcr= 0, d = ∞c = 25, W = 0.9 µm, RTip=0.5 µm

𝐺𝑇𝑜𝑡𝑎𝑙=2𝑒2

h(𝑎+𝑏)𝑐𝑎+𝑏+𝑐

G (2e2/h)Qualitative model

µ

Dashed lines are guides to the eye

Model vs. experiment

Model G (2e2/h) G (2e2/h)Experiment

1D profiles along red lines shown in the previous slide

Model vs. experiment

Magnetic field dependence

Vtip= -8.0 V

Vcgate= -1.0 V

B = 0 mT

dG/dx

X (µm)

1 µmy

(µm

)

Vtip= -8.0 V

Vcgate= -1.0 V

B = 50 mT

Magnetic field dependencedG/dx

X (µm)

1 µmy

(µm

)

Magnetic field dependence

Vtip= -8.0 V

Vcgate= -1.0 V

B = 100 mT

dG/dx

X (µm)

1 µmy

(µm

)

Vtip= -8.0 V

Vcgate= -1.0 V

B = 200 mT

Magnetic field dependencedG/dx

X (µm)

1 µmy

(µm

)

Magnetic field dependence

Vtip= -8.0 V

Vcgate= -1.0 V

B = 300 mT

dG/dx

X (µm)

1 µmy

(µm

)

Magnetic field dependence

Vtip= -8.0 V

Vcgate= -1.0 V

B = 500 mT

dG/dx

X (µm)

1 µmy

(µm

)

Magnetic field dependence

Vtip= -8.0 V

Vcgate= -1.0 V

B = 0 mT

dG/dx

X (µm)

1 µmy

(µm

)

Magnetic field dependence

Dr. Dietmar Weinmann, Strasbourg, France

dG/dx

dG/dx

Summary (experimental observations)

QPC:

• Backscattering effect

• Interference effect

Ballistic stadium:

• Two fringe patterns

• Conductance fluctuations

1 µm500 nm

1 µm

• Center of the stadium

• Positions of the lens-shaped regions

• Magnetic field dependence

Summary (experimental features not covered by the model)

THANK YOU

Numerical simulations (top panel) vs. experiment (bottom panel)

RTip=0.05 µm RTip=0.5 µm RTip=1 µm

Vtip = - 8 VVtip = - 6 VVtip = - 4 V

G ≈ 17× 2e2/h without the tip

Features not explained by simulations

• A region of reduced conductance in the center of the stadium at low tip biases (experiment)

• Positions of the lens-shaped regions:

inside the stadium in the experiment

in the centers of the constrictions in the simulations

Numerical simulations (B = 0 mT):same as in the previous slide, but the color scales are different

RTip=0.05 µm RTip=0.5 µm

RTip=1 µm

SGM technique

Gating effect

μS μD

EnergyTop gates

2DEG

Tip

-0.8 -0.7 -0.6 -0.5 -0.40

1

2

3

4

5

6

7

Con

duct

ance

, G

(2e

2 /h)

Gate voltage, Vg (V)

Tip-inducedpotential

D. A. Wharam et al., 1988B. J. van Wees et al., 1988

Influence of the tip on the conductance

-0.9 -0.8 -0.7 -0.60

1

2

3 V

Tip = 0 V, B = 0 mT

VTip

= -6 V, B = 0 mT

VTip

= -6 V, B = 25 mT

G (

2e2 /h

)

Vg (V)

(a)

Central branch Side branchOff branch

-0.9 -0.8 -0.7 -0.60

1

2

3

G (

2e2 /h

)

Vg (V)

(c)

-0.9 -0.8 -0.7 -0.60

1

2

3

G (

2e2 /h

)

Vg (V)

(b)

2e2/h

Scanning inside the stadium

Vtip=-8.0 V

Vcgate=-1.0 VVQPC=0 V

Scanning inside the stadium

Vcgate=-1.0 VVQPC=-0.38 VB=0 mT

Vtip=-8.0 V

Profiles

Vtip=-8.0 V

Vcgate=-1.0 V

B=0 mT

A B

A

B

Left QPC is biased, 3 modes. This is the case only in this slide.

Profiles

Vtip=-8.0 V

Vcgate=-1.0 V

B=300 mT

I (nA)

A B

A

B

Profiles

Vtip=-8.0 V

Vcgate=-1.0 V

B=500 mT

I (nA)

A

B

A B

Magnetoresistance measurements

0 1 2 3 4 5

0

5

10

15

20

25

30

= 5 = 4

= 3

= 2

R (

kOhm

)

B (T)

= 1

= 6

Magnetoresistance measurements

0 40 80 120 160 200 240 280 320

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-2.5 V

-2,0 V

-1,5 V-1,2 V-1,0 V-0,8 V

-0,5 V

R (

kOhm

)

B (mT)

0 V

B (mT) rc (um)

120 0.48

100 0.58

80 0.72

60 0.96

40 1.44

10 5.75

Stadiumvoltage

Magnetic focusing

80 mT100 mT

50 mTB (mT) rc (um)

120 0.48

100 0.58

80 0.72

60 0.96

40 1.44

10 5.75

Summary (experimental observations)Scanning gate microscopy on a quantum point contact:

• Imaging electron backscattering• Observation of branches and interference fringes• Detailed investigation of the branching behaviour• Strongly varying interference fringe spacing

Scanning gate microscopy on a ballistic stadium:

• Two fringe pattern close to the constrictions• Measurements at high magnetic fields• Proposed model explains some of the observed

features, but not all of them