Electron backscattering in a cavity: Ballistic and coherent effects

A. A. Kozikov, D. Weinmann, C. Rössler, T. Ihn, K. Ensslin, C. Reichl, and W. Wegscheider

Phys. Rev. B 94, 195428 – Published 17 November 2016

Abstract

Numerous experimental and theoretical studies have focused on low-dimensional systems locally perturbed by the biased tip of a scanning force microscope. In all cases either open or closed weakly gate-tunable nanostructures have been investigated, such as quantum point contacts, open or closed quantum dots, etc. We study the behavior of the conductance of a quantum point contact with a gradually forming adjacent cavity in series under the influence of a scanning gate. Here, an initially open quantum point contact system gradually turns into a closed cavity system. We observe branches and interference fringes known from quantum point contacts coexisting with irregular conductance fluctuations. Unlike the branches, the fluctuations cover the entire area of the cavity. In contrast to previous studies, we observe and investigate branches under the influence of the confining stadium potential, which is gradually built up. We find that the branches exist only in the area surrounded by cavity top gates. As the stadium shrinks, regular fringes originate from tip-induced constrictions leading to quantized conduction. In addition, we observe arclike areas reminiscent of classical electron trajectories in a chaotic cavity. We also argue that electrons emanating from the quantum point contact spread out like a fan leaving branchlike regions of enhanced backscattering.

Received 17 July 2016
Revised 1 November 2016

DOI:https://doi.org/10.1103/PhysRevB.94.195428

Physics Subject Headings (PhySH)

Ballistic transport Electrical conductivity Quantum interference effects Semiconductors

Point contacts Two-dimensional electron gas

Hall bar Scanning probe microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. A. Kozikov¹, D. Weinmann², C. Rössler¹, T. Ihn¹, K. Ensslin¹, C. Reichl¹, and W. Wegscheider¹

¹Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
²Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, 23 rue du Loess, F-67034 Strasbourg, France

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Issue

Vol. 94, Iss. 19 — 15 November 2016

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Images

Figure 1
(a) Room-temperature atomic force microscopy image of the studied sample. Pairs of top gates form the LQPC, RQPC, and stadium (TG1 and TG2) and are marked by different colors. The tip-induced depletion region (bright green) backscatters electrons injected into the stadium from the left QPC (white arrows). The ac current flows between the source “ $S$ ” and drain “ $D$ ” contacts. (b) Schematics of an SGM setup. A conical tip (dark red) is placed above the surface (blue) inside the stadium (yellow metallic top gates). The negatively biased tip produces a strong perturbation in the two-dimensional electron gas (2DEG). Below the tip the 2DEG is completely depleted (a circular region below the tip). Such a disk acts as a movable backscatterer. The long-range nature of the tip-induced potential is indicated as a color gradient between the tip-depleted region and the top gates. The greenish area around the top gates marks the depletion around them.
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Figure 2
Evolution of the QPC conductance $G (x, y)$ (upper panel) and its numerical derivative $d G (x, y) / d x$ (lower panel) with respect to the scan direction $x$ as the voltage applied to the stadium $V_{g}$ varies from 0 to $- 1 V$ . Arrows in (a) and the lower panel and yellow ellipses in the lower panel mark branches (fringes) of types $A$ and $B$ , respectively. Dashed-dotted lines in (b) and (f) indicate regions where the one-dimensional (1D) conductance is studied quantitatively. The label “0” near one end of this line marks the beginning of the 1D cuts. The curved dashed lines in (e)–(h) mark the position of the arclike areas of type $C$ . The QPC is biased to the third conductance plateau without the tip and the stadium. Biased top gates are shown as solid lines. The thickness of the top gates in (g) and (h) is enhanced to illustrate the depletion zone for negative gate voltages. Brown, green, and blue contour lines in the top panel correspond to the constant conductance of 1.5, 2, and $2.5 \times 2 e^{2} / h$ . The green contour lines in (e) in the arclike areas are intentionally absent to avoid confusion.
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Figure 3
(a) $G$ as a function of distance $r$ along the white dashed-dotted line shown in Figs. 2 and 2 for different $V_{g}$ . $G$ in a smaller range of $r$ (zoom in) is given in the inset. Interference fringes at $r < 0.8 μ m$ and conductance fluctuations at $r > 0.8 μ m$ are visible when the stadium is formed (blue curve). (b) $d G (x, y) / d x$ along the white dashed-dotted line shown in Figs. 2 and 2. Interference fringes and conductance fluctuations are more clearly visible at small and large $r$ , respectively. (c) $d G (x, y) / d x$ across interference fringes in region B1 indicated in Figs. 2 and 2 at different $V_{g}$ . (d) The same as in (c) but in region B2 [Figs. 2 and 2].
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Figure 4
(a) A closeup of the upper curved branch in Fig. 2: numerical derivative of the conductance as a function of tip position. (b) A 1D cut along the pink polyline in (a). Zero in the plotted curve is marked by the label 0 in (a). (c)–(e) Simulations of the conductance as a function of tip position for (c) a hard wall, (d) Lorentzian tip-induced potential, and (e) including disorder. The gray solid lines outline the top gate TG1.
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