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Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider.

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Presentation on theme: "Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider."— Presentation transcript:

1 Imaging transmission of nanostructures in a high-mobility heterostructure Aleksey Kozikov Clemens Rössler Thomas Ihn Klaus Ensslin C. Reichl W. Wegscheider Local electron transport Diffusive/ballistic transport Classical/quantum phenomena

2 Motivation Ultra high-mobility: l p >> 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?

3 Motivation QPC 2DEG x y Conductance, G M. Topinka et al. Nature 410, (2001)

4 Motivation 300 K 115 K 0.24 K Local relocation of charge between donor sites Scannell et al. PRB 85, (2012)

5 Motivation Wilkinson et al. Nature 380, 608 (1996) Conductance through a tunneling diode

6 Motivation Experimental dataFiltered data Crook et al. PRL 91, (2003)

7 Motivation Experimental dataTheoryFiltered data No one-to-one correspondence Aoki et al. PRL 108, (2012)

8 Sample n = 1.2 × m -2 E F = 4 meV λ F = 72 nm µ = 850 m 2 /Vs l p = 49 µm D Stadium = 3 µm Excellent wafers: C. Reichl W. Wegscheider ETH Zurich Golden top gates QPC Ballistic stadium 2DEG 1 µm

9 Quantum point contact Top gates 2DEG Electron flow D. A. Wharam et al., 1988 B. J. van Wees et al., 1988

10 Energy Tip Top gates 2DEG SGM technique Backscattering effect Landauer-Büttiker theory of transport d D. A. Wharam et al., 1988 B. J. van Wees et al., 1988

11 Electron backscattering through the QPC 3 rd plateau V tip = -6.0 V d = 70 nm 1 µm x y Differential conductance, dG/dx arXiv:

12 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 (µm) Scanning gate microscopy on a QPC arXiv: Small-angle scattering

13 V tip = -8.0 V V stadium = -0.5 V Scanning gate microscopy on a stadium dG/dx X (µm) 1 µm y (µm)

14 Scanning gate microscopy on a stadium dG/dx V tip = -8.0 V V stadium = -0.8 V X (µm) 1 µm y (µm)

15 Scanning gate microscopy on a stadium dG/dx V tip = -8.0 V V stadium = -2.0 V X (µm) 1 µm y (µm)

16 V tip = -8.0 V V stadium = -0.8 V Scanning gate microscopy on a stadium G (2e 2 /h)dG/dx 1 µm

17 500 nm Scanning gate microscopy on a stadium dG/dx

18 Scanning gate microscopy on a stadium dG/dx G (2e 2 /h)dG/dx

19 a b c d Qualitative model

20 a b c d contact resistance R cr

21 Assumptions: R cr = 0, d = c = 25, W = 0.9 µm, R Tip =0.5 µm G (2e 2 /h) Qualitative model

22 µ Dashed lines are guides to the eye Model vs. experiment ModelG (2e 2 /h) Experiment

23 1D profiles along red lines shown in the previous slide Model vs. experiment

24 Magnetic field dependence V tip = -8.0 V V cgate = -1.0 V B = 0 mT dG/dx X (µm) 1 µm y (µm)

25 V tip = -8.0 V V cgate = -1.0 V B = 50 mT Magnetic field dependence dG/dx X (µm) 1 µm y (µm)

26 Magnetic field dependence V tip = -8.0 V V cgate = -1.0 V B = 100 mT dG/dx X (µm) 1 µm y (µm)

27 V tip = -8.0 V V cgate = -1.0 V B = 200 mT Magnetic field dependence dG/dx X (µm) 1 µm y (µm)

28 Magnetic field dependence V tip = -8.0 V V cgate = -1.0 V B = 300 mT dG/dx X (µm) 1 µm y (µm)

29 Magnetic field dependence V tip = -8.0 V V cgate = -1.0 V B = 500 mT dG/dx X (µm) 1 µm y (µm)

30 Magnetic field dependence V tip = -8.0 V V cgate = -1.0 V B = 0 mT dG/dx X (µm) 1 µm y (µm)

31 Magnetic field dependence QPCSGM116 5 th cooldown Dr. Dietmar Weinmann, Strasbourg, France dG/dx

32 Summary (experimental observations) QPC: Backscattering effect Interference effect Ballistic stadium: Two fringe patterns Conductance fluctuations 1 µm 500 nm 1 µm

33 Center of the stadium Positions of the lens-shaped regions Magnetic field dependence Summary (experimental features not covered by the model)

34 THANK YOU

35 Numerical simulations (top panel) vs. experiment (bottom panel) R Tip =0.05 µm R Tip =0.5 µm R Tip =1 µm V tip = - 8 VV tip = - 6 V V tip = - 4 V G 17× 2e 2 /h without the tip

36 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

37 Numerical simulations (B = 0 mT): same as in the previous slide, but the color scales are different R Tip =0.05 µmR Tip =0.5 µm R Tip =1 µm

38 SGM technique Gating effect μSμS μDμD Energy Top gates 2DEG Tip Tip-induced potential D. A. Wharam et al., 1988 B. J. van Wees et al., 1988

39 Influence of the tip on the conductance

40 Scanning inside the stadium V tip =-8.0 V V cgate =-1.0 V V QPC =0 V

41 Scanning inside the stadium V cgate =-1.0 V V QPC =-0.38 V B=0 mT V tip =-8.0 V

42 Profiles V tip =-8.0 V V cgate =-1.0 V B=0 mT AB A B Left QPC is biased, 3 modes. This is the case only in this slide.

43 Profiles V tip =-8.0 V V cgate =-1.0 V B=300 mT I (nA) AB A B

44 Profiles V tip =-8.0 V V cgate =-1.0 V B=500 mT I (nA) A B AB

45 Magnetoresistance measurements

46 B (mT)rc (um) Stadium voltage

47 Magnetic focusing 80 mT 100 mT 50 mT B (mT)rc (um)

48 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


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