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