Scanning gate microscopy and individual control of edge-state transmission through a quantum point contact
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1 Scanning gate microscopy and individual control of edge-state transmission through a quantum point contact Stefan Heun NEST, CNR-INFM and Scuola Normale Superiore, Pisa, Italy
2 Coworkers NEST, Pisa, Italy: Nicola Paradiso Stefano Roddaro Lucia Sorba Fabio Beltram Bell Labs, Murray Hill, USA Loren Pfeiffer Ken West TASC, Trieste, Italy Giorgio Biasiol
3 Outline Introduction Scanning Gate Microscopy Control of Edge State Transmission through a Quantum Point Contact
4 Motivation Interference phenomena Manifestation of wave nature of electrons Applications in quantum information technology 2DES in the Quantum Hall regime Large electronic coherence length Edge channel chiral transport Solid state system to study interference
5 2Dimensional Electron System B
6 Hall bar geometry Measurement of longitudinal and transversal resistance K. von Klitzing et al.: Physik Journal 4 (2005) No.6 p.37.
7 Hall effect Drude model: R xy = proportional to B R xx = costant in B K. von Klitzing et al.: Physik Journal 4 (2005) No.6 p.37.
8 Quantum Hall Effect Behaviour observed at low temperature in high mobility samples: Plateaux in R xy Minima in R xx Quantum Hall Effect: deviations from Drude model observed around B = nh / νe ν: filling factor integer / fractional QHE K. von Klitzing et al.: Physik Journal 4 (2005) No.6 p.37.
9 The Nobel prize in Physics 1985: integer QHE 1998: fractional QHE
10 Introduction to edge channels edge bulk y x x
11 Introduction to edge channels edge: 1D one-way conductor bulk: insulator y x x Quantization of energy levels (Landau levels) Gap for excitation in the bulk Transport via edge states
12 How to probe edge channels?
13 How to probe edge channels?
14 How to probe edge channels?
15 Quantum Point Contact V gate 1.7µm Conductance quantization
16 Mach-Zehnder interferometer Y. Ji et al., Nature 422 (2003) 415.
17 Mach-Zehnder interferometer V Y. Ji et al., Nature 422 (2003) 415.
18 Mach-Zehnder interferometer Y. Ji et al., Nature 422 (2003) 415.
19 Two-particle Aharonov-Bohm interferometer Hanbury-Brown-Twiss interferometer Topology limits complexity to max. 2 interferometers I. Neder et al., Nature 448 (2007) 333.
20 Multichannel architecture for Quantum Hall interferometry V. Giovannetti et al., Phys. Rev. B 77 (2008)
21 Challenges Complex edge structure Control of interaction between different edge channels Use SGM to control trajectory and interaction of edge channels Based on results of S. Roddaro on QPC in QH regime: PRL 95 (2005) PRL 103 (2009)
22 Scanning Gate Microscopy AFM at 400 mk with B < 9 Tesla. Tip at negative bias (local gate - locally depletes the 2DEG), no current flows SGM performed in constant height mode (10-50 nm above surface), no strain M. A. Topinka et al.: Science 289 (2000) 2323.
23 LT-AFM system for SGM
24 Customized cryogenic microscope System allows standard AFM and STM operation AFM non-optical detection scheme (tuning fork) With vibration and noise isolation system 3 He insert (300 mk) 9 T cryomagnet
25 Oct 2007: First cooldown
26 AFM Head Positioner (range in xyz > 6 mm) allow to locate features on the sample with µm precision Scan range: 42µm x 42µm x RT 8.5µm x 8.5µm x 300 mk Temperature measurement (RuO 2 ) close to sample Drift < 1 nm / h Temperature stability Delta T / T < 5% for hours, even at max. B field Noise in z at 300 mk: 1nm
27 Tuning Fork
28 AFM at room temperature
29 AFM at low temperature T = 350 mk B = 0 T B = 9 T
30 Sample holder for transport measurements Base mounted on AFM scanner Contact via pogo pins Chip carrier holds sample
31 Tip sample geometry
32 Sample temperature calibration Coulomb Blockade Thermometer (CBT) He 3 pot (RuOx): Close to sample (RuOx): Sample (CBT): 290 mk 365 mk 410 mk
33 STM Head High stability positioner Linear travel in xyz: 5 mm Step size K Max. speed 1 mm / s Piezo Tube Scanner Smaller scan range: 2 um in xy, 400 nm in z. Higher stability and resolution Temperature measurement (RuO 2 ) close to sample
34 320 mk, sample HOPG, tip PtIr B = 0 T B = 9 T 21/10/2007
35 Samples High-mobility AlGaAs heterostructures Depth d = 55 nm Electron density n = 3.37 x cm -2 Dark mobility μ = 2.62 x 10 6 cm 2 /V s Fermi wavelength λ F = 43 nm Mean free path L = 25 μm Schottky split-gate QPC Ti / Au bilayer (10 nm / 20 nm) Gap 300 nm
36 Hall-bar samples 1900 μm x 300 μm
37 Hall-bar samples
38 Hall-bar samples
39 Hall-bar samples
40 Hall-bar samples
41 Hall-bar samples 3 rd plateau
42 QPC at 3 rd plateau G = 6 e 2 /h nm 0.00 G = 0
43 QPC at 2 nd plateau G = 6 e 2 /h 5.50 G = 4 e 2 /h 600nm 0.00 G = 0
44 QPC at 1 st plateau G = 6 e 2 /h 5.50 G = 2 e 2 /h 600nm 0.00 G = 0
45 QPC at 3 rd plateau G = 6 e 2 /h nm 0.00 G = 0
46 QPC at 2 nd plateau 600nm
47 QPC at 1 st plateau 600nm
48 Branched flow of electrons No magnetic field (B = 0) QPC conductance G = 6 e 2 /h (3 rd plateau) Tip voltage V tip = -5 V, height h tip = 10 nm see also M. A. Topinka et al., Nature 410 (2001) 183.
49 Tip-induced backscattering
50 Branched flow of electrons No magnetic field (B = 0) QPC conductance G = 6 e 2 /h (3 rd plateau) Tip voltage V tip = -5 V, height h tip = 10 nm see also M. A. Topinka et al., Nature 410 (2001) 183.
51 Tip-induced backscattering
52 Interference fringes 400nm 100nm
53 Impact of small magnetic field G43: 0 mt G45: 5 mt 400nm 400nm
54 SGM in the Quantum Hall regime Tip voltage V tip = -5 V, height = 30 nm
55 Magnetoresistance
56 Selective control of edge channel trajectories by SGM Bulk filling factor ν=4 B = 3.04 T 2 spin-degenerate edge channels gate-region filling factors g 1 = g 2 = 0 600nm ee 2 /h 2 /h e 2 /h 0.0 e 2 /h
57 Determine the local filling factor v bulk = 4
58 Determine the local filling factor 0 v bulk = 4
59 Determine the local filling factor Depleted (g = 0) 0 v bulk = 4 0
60 Determine the local filling factor Depleted (g = 0) 0 v bulk = 4 0 Sweep one gate
61 Determine the local filling factor Depleted (g = 0) 0 v bulk = 4 0 Sweep one gate
62 Determine the local filling factor Depleted (g = 0) 0 v bulk = 4 0 Sweep one gate
63 Asymmetrical gate bias 600nm g 1 = 0, g 2 = 2 Only inner edge channel can be backscattered Outer edge has no counterpart for backscattering G min = 2 e 2 /h
64 Asymmetrical gate bias 600nm 600nm
65 Identical filling factors g 1 = g 2 = 2 600nm 600nm 600nm
66 Edge state transmission for ν = 6 V tip = -3 V Bulk filling factor ν = 6 (3 spin-degenerate edge channels)
67 Summary Lower bound for conductance determined by number of paired edges Unpaired edge channels unaffected by tip gating Our results are a crucial first step for implementation of multi-edge beam mixers and interferometers
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