Imaging the lateral shift of a quantum point contact using scanning gate microscopy

We perform scanning-gate microscopy on a quantum-point contact. It is defined in a high-mobility two-dimensional electron gas of an AlGaAs/GaAs heterostructure, giving rise to a weak disorder potential. The lever arm of the scanning tip is significantly smaller than that of the split gates defining the conducting channel of the quantum-point contact. We are able to observe that the conducting channel is shifted in real space when asymmetric gate voltages are applied. The observed shifts are consistent with transport data and numerical estimations.

Figure 1

(a) Transconductance of the QPC from Ref. 14 at $T=1.3\mathrm{K}$. Up to 13 conductance steps appear as hyperbolic-shaped features in the plane of the two top gates. We define the asymmetry in top-gate voltages as $\Delta V_{\mathrm{G}}:=V_{\mathrm{LG}}-V_{\mathrm{RG}}$. The white circles are points at the indicated values of $\Delta V_{\mathrm{G}}$. The quantities ${\delta }_{\mathrm{LG}}$ and ${\delta }_{\mathrm{RG}}$ are the distances of the conducting QPC channel to the left and right top gates as described in the main text below. Inset: Topography of a nominally identical QPC (discussed in Ref. 14). The channel formed by the two top gates with applied voltages $V_{\mathrm{RG}}$ and $V_{\mathrm{LG}}$ has a width of 200 nm. (b) Depletion curve of the QPC under investigation here as a function of top-gate voltage. Depletion under the top gates is reached for $V_{\mathrm{G}}⩽-1.35\mathrm{V}$. Conductance steps are smeared out because of the rather high temperature of $T\approx 10\mathrm{K}$. Close to pinch-off, a weak 0.7 anomaly is observed. The QPC is pinched off at $V_{\mathrm{G}}\approx -2.35\mathrm{V}$. (c) Conductance of the QPC as a function of tip voltage $V_{\mathrm{tip}}$ for a tip height of 50 nm above the gates and $V_{\mathrm{G}}=-2.2\mathrm{V}$.

Figure 2

(a) Scanning-gate image of the QPC for a source-drain bias of $100\mu \mathrm{V}$, $V_{\mathrm{G}}=-2\mathrm{V}$, and $V_{\mathrm{tip}}=-3\mathrm{V}$. The current $I$ through the QPC is shown in color code as a function of tip position. The dotted lines trace the outline of the metallic top gates. (b) Line cuts along the vertical and the horizontal dashed lines in (a). They are offset from each other for clarity. The current decreases when the tip approaches the QPC as is expected for a negatively charged tip. The unexpected enhancement of current in the QPC shows up as a local maximum. The (blue) data points are fitted with a Lorentzian function (solid lines) with the indicated widths.

Figure 3

(a) Line scans of the tip along the QPC axis [dashed line in Fig. 1a, scale is given in panel (b), $V_{\mathrm{tip}}=-3\mathrm{V}$]. The gate asymmetry is changed along the vertical axis such that $V_{\mathrm{LG}}=-2.25\mathrm{V}+\Delta {\mathrm{V}}_{\mathrm{G}}/2$, and the current through the QPC is given in color code [arbitrary units, color palette as in Fig. 2a but for each line the average value was subtracted]. The position $x_{\mathrm{spot}}$ of the spot of enhanced current is independent of $\Delta V_{\mathrm{G}}$ as the vertical dashed line shows whereas the overall decrease in current is tilted to the left for more positive $\Delta V_{\mathrm{G}}$. This becomes clearer in panel (b) where we present line cuts extracted from the measurement shown in (a) for the indicated gate-voltage asymmetries: The peak of enhanced current is at the same tip position for all voltages but the outer envelope is shifted to the left for increasing asymmetry. (c) Shift of the QPC channel (red circles) for different gate-voltage asymmetries $\Delta V_{\mathrm{G}}$ deduced from panel (a) compared with the shift estimated from the transport experiment presented in Fig. 1a (green squares) and with theory (blue stars).