Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens...
-
Upload
gisselle-pennix -
Category
Documents
-
view
215 -
download
1
Transcript of Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens...
![Page 1: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/1.jpg)
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
![Page 2: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/2.jpg)
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?
![Page 3: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/3.jpg)
Motivation
QPC
2DEG
x
y
Conductance, G
M. Topinka et al. Nature 410, 183-186 (2001)
![Page 4: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/4.jpg)
Motivation
300 K115 K0.24 K
Local relocation of charge between donor sites
Scannell et al. PRB 85, 195319 (2012)
![Page 5: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/5.jpg)
Motivation
Wilkinson et al. Nature 380, 608 (1996)
Conductance through a tunneling diode
![Page 6: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/6.jpg)
MotivationExperimental data Filtered data
Crook et al. PRL 91, 246803 (2003)
![Page 7: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/7.jpg)
MotivationExperimental data TheoryFiltered data
No one-to-one correspondenceAoki et al. PRL 108, 136804 (2012)
![Page 8: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/8.jpg)
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
![Page 9: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/9.jpg)
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)
![Page 10: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/10.jpg)
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)
![Page 11: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/11.jpg)
Electron backscattering through the QPC
3rd plateau
Vtip= -6.0 Vd = 70 nm
1 µm
xy
Differential conductance, dG/dx
arXiv:1206.1371
![Page 12: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/12.jpg)
• 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
![Page 13: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/13.jpg)
Vtip= -8.0 V
Vstadium= -0.5 V
Scanning gate microscopy on a stadiumdG/dx
X (µm)
1 µmy
(µm
)
![Page 14: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/14.jpg)
Scanning gate microscopy on a stadiumdG/dx
Vtip= -8.0 V
Vstadium= -0.8 V
X (µm)
1 µmy
(µm
)
![Page 15: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/15.jpg)
Scanning gate microscopy on a stadiumdG/dx
Vtip= -8.0 V
Vstadium= -2.0 V
X (µm)
1 µmy
(µm
)
![Page 16: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/16.jpg)
Vtip= -8.0 V Vstadium= -0.8 V
Scanning gate microscopy on a stadiumG (2e2/h)dG/dx
1 µm 1 µm
![Page 17: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/17.jpg)
500 nm
Scanning gate microscopy on a stadiumdG/dx
![Page 18: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/18.jpg)
Scanning gate microscopy on a stadium
dG/dx
G (2e2/h)dG/dx
![Page 19: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/19.jpg)
a
b
c
d
Qualitative model
![Page 20: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/20.jpg)
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
![Page 21: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/21.jpg)
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
![Page 22: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/22.jpg)
µ
Dashed lines are guides to the eye
Model vs. experiment
Model G (2e2/h) G (2e2/h)Experiment
![Page 23: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/23.jpg)
1D profiles along red lines shown in the previous slide
Model vs. experiment
![Page 24: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/24.jpg)
Magnetic field dependence
Vtip= -8.0 V
Vcgate= -1.0 V
B = 0 mT
dG/dx
X (µm)
1 µmy
(µm
)
![Page 25: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/25.jpg)
Vtip= -8.0 V
Vcgate= -1.0 V
B = 50 mT
Magnetic field dependencedG/dx
X (µm)
1 µmy
(µm
)
![Page 26: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/26.jpg)
Magnetic field dependence
Vtip= -8.0 V
Vcgate= -1.0 V
B = 100 mT
dG/dx
X (µm)
1 µmy
(µm
)
![Page 27: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/27.jpg)
Vtip= -8.0 V
Vcgate= -1.0 V
B = 200 mT
Magnetic field dependencedG/dx
X (µm)
1 µmy
(µm
)
![Page 28: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/28.jpg)
Magnetic field dependence
Vtip= -8.0 V
Vcgate= -1.0 V
B = 300 mT
dG/dx
X (µm)
1 µmy
(µm
)
![Page 29: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/29.jpg)
Magnetic field dependence
Vtip= -8.0 V
Vcgate= -1.0 V
B = 500 mT
dG/dx
X (µm)
1 µmy
(µm
)
![Page 30: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/30.jpg)
Magnetic field dependence
Vtip= -8.0 V
Vcgate= -1.0 V
B = 0 mT
dG/dx
X (µm)
1 µmy
(µm
)
![Page 31: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/31.jpg)
Magnetic field dependence
Dr. Dietmar Weinmann, Strasbourg, France
dG/dx
dG/dx
![Page 32: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/32.jpg)
Summary (experimental observations)
QPC:
• Backscattering effect
• Interference effect
Ballistic stadium:
• Two fringe patterns
• Conductance fluctuations
1 µm500 nm
1 µm
![Page 33: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/33.jpg)
• Center of the stadium
• Positions of the lens-shaped regions
• Magnetic field dependence
Summary (experimental features not covered by the model)
![Page 34: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/34.jpg)
THANK YOU
![Page 35: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/35.jpg)
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
![Page 36: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/36.jpg)
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
![Page 37: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/37.jpg)
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
![Page 38: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/38.jpg)
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
![Page 39: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/39.jpg)
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
![Page 40: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/40.jpg)
Scanning inside the stadium
Vtip=-8.0 V
Vcgate=-1.0 VVQPC=0 V
![Page 41: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/41.jpg)
Scanning inside the stadium
Vcgate=-1.0 VVQPC=-0.38 VB=0 mT
Vtip=-8.0 V
![Page 42: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/42.jpg)
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.
![Page 43: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/43.jpg)
Profiles
Vtip=-8.0 V
Vcgate=-1.0 V
B=300 mT
I (nA)
A B
A
B
![Page 44: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/44.jpg)
Profiles
Vtip=-8.0 V
Vcgate=-1.0 V
B=500 mT
I (nA)
A
B
A B
![Page 45: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/45.jpg)
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
![Page 46: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/46.jpg)
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
![Page 47: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/47.jpg)
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
![Page 48: Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.](https://reader034.fdocuments.in/reader034/viewer/2022042814/55164d39550346a2698b4a49/html5/thumbnails/48.jpg)
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