Figure 1

(a) AFM image of the open QD sample fabricated by electron beam lithography and wet etching. The dotted rectangular ($860\mathrm{nm}\times 1420\mathrm{nm}$) region highlights the scanning area in the SGM observations. On top of the QD, a tip is applied in lift mode with a certain distance (50 nm) with respect to the wafer surface. The tip is biased typically with $-6\mathrm{V}$ in dc and causes depletion in the two-dimensional electron gas plane. Note that both perpendicular sides of the dot can be used as side gates. (b) Magneto resistance of the open QD measured without a biased tip. At certain magnetic field values, maxima (at $B=100\mathrm{mT}$, $B=240\mathrm{mT}$) and minima ($B=180\mathrm{mT}$) arise. SGM image shows (c) the change of resistance $R$ across the open QD (bright: high $R$), (d) the variation of the conductance $\Delta G$ (bright: positive $\Delta G$, dark: negative: $\Delta G$), and (e) $\Delta G^2$ corresponding to the square of the conductance variation $\Delta G$ (bright: high $\Delta G^2$). Below: The corresponding line profiles for $R$, $\Delta G$, and $\Delta G^2$ are shown for clarity.Reuse & Permissions

Figure 2

Comparison of classical trajectories, scarred wave function, and $\Delta G^2$ images at different magnetic field values. Above: A single featured trajectory and probability density superimposed on the $\Delta G^2$ image. Below: Trajectory calculated for various entrance angles (about $-90°$ to $+90°$) including the featured trajectory (in red), probability density, and $\Delta G^2$ image, all shown as separated figures. Dashed lines in the image are used as a guide for the eye. (a) $B=0\mathrm{mT}$, featured single trajectory with an entrance angle of 0°. (b) $B=100\mathrm{mT}$, featured single trajectory with an entrance angle of 0°. (c) $B=180\mathrm{mT}$, featured single trajectory with an entrance angle of $-5.7°$. (d) $B=240\mathrm{mT}$, featured single trajectory with an entrance angle of 17.2°. Color code: High and low probability density correspond to grey and black, respectively. High and low $\Delta G^2$ corresponds to bright and dark, respectively. The size of each panel is $1000\mathrm{nm}\times 1500\mathrm{nm}$.Reuse & Permissions

Figure 3

(a) Topographic image from the open QD. Circles show schematically the various measurement positions in $y$ between $-600$ and $+600\mathrm{nm}$ at $x=0\mathrm{nm}$. (b) Magneto-conductance oscillations and the contour plot measured at the different tip positions shown in (a). Each curve is plotted with certain offsets. High and low conductance corresponds to bright and dark, respectively, as shown in a color-scale bar. The amplitude of the conductance oscillations curve is within $\pm 0.02e^2/h$ which is the same order of conductance oscillations without the tip shown at the top. (c) and (d) are $\Delta G^2$ images obtained with $V_{\mathrm{tip}}=-3\mathrm{V}$ and $-6\mathrm{V}$, respectively, at $B=0\mathrm{T}$ and $V_s=0\mathrm{V}$.Reuse & Permissions

Figure 4

$\Delta G^2$ images obtained at zero magnetic field for different side gate voltages of $V_s=$ (a) 0 V, (b) $-0.5\mathrm{V}$, (c) $-1.0\mathrm{V}$, and (d) $-1.5\mathrm{V}$, respectively. These figures are plot in the same color scale. White circles show robust spots up to $-1.5\mathrm{V}$. (e) Conductance $G$ across the open QD as a function of the side gate voltage $V_s$. By increasing the negative voltage on the side gate, the conductance decrease due to depletion at the constriction regions. An indication that a less negative $V_s$ is related to a stronger coupling to the environment.Reuse & Permissions