Local signatures of electron-electron scattering in an electronic cavity

We image equilibrium and nonequilibrium transport through a two-dimensional electronic cavity using scanning gate microscopy. Injecting electrons into the cavity through a quantum point contact close to equilibrium, we raster scan a weakly invasive tip above the cavity region and measure the modulated conductance through the cavity. Varying the electron injection energy between $\pm 2\mathrm{meV}$, we observe that conductance minima turn into maxima beyond an energy threshold of $\pm 0.6\mathrm{meV}$. This observation bears similarity to previous measurements by Jura et al. [Phys. Rev. B 82, 155328 (2010)], who used a strongly invasive tip potential to study electron injection into an open two-dimensional electron gas. This resemblance suggests a similar microscopic origin based on electron-electron interactions.

Figure 1

(a) Scanning electron micrograph of the open resonator structure with Schottky gates (light gray) on a GaAs-surface (dark gray). The cavity area is depicted by the blue standing wave. The black squares denote the source (S) and drain (D) ohmic contacts. This micrograph has also been published in Ref. [17] and the Supplementary Materials of Ref. [21]. (b) Numerical derivative $dG/d{V}_{\mathrm{qpc}}$ of the differential conductance $G$ as a function of $V_{\mathrm{sd},\mathrm{dc}}$ and $V_{\mathrm{qpc}}$. Red arrows mark the cavity modes. The dashed orange line corresponds to the QPC voltage used for all following measurements. The data for $|V_{\mathrm{sd},\mathrm{dc}}|>1\mathrm{mV}$ are obtained with lower resolution in bias voltage and are numerically smoothened to increase the visibility of the diamond-shaped pattern. An excerpt from this data has also been published in the Supplementary Material of Ref. [21]. (c) Spatial image of the conductance $G(x,y)$ in the cavity as a function of the tip position for $V_{\mathrm{tip}}=-1\mathrm{V}$ and $V_{\mathrm{cav}}=-400\mathrm{mV}$. Dotted lines outline the position of the Schottky gates. The data presented in Fig. 2 are obtained along the red dashed line.

Figure 2

Differential conductance $G(x,V_{\mathrm{sd},\mathrm{dc}})$ along the dashed red line in Fig. 1. (a) Raw data. (b) Linewise conductance difference $\mathrm{\Delta }G\left(x\right)$ as a function of the tip position $x$ along the red line in (a) for small steps in $V_{\mathrm{sd},\mathrm{dc}}$. The red curve denotes the conductance at $V_{\mathrm{sd},\mathrm{dc}}=0\mathrm{mV}$ and the lines are offset with respect to each other. Black dashed guides to the eye denote three exemplary minimum-to-maximum transitions. The thick line marks the conductance modulations at the transition voltage.

Figure 3

Differential conductance $G(V_{\mathrm{cav}},V_{\mathrm{sd},\mathrm{dc}})$ in absence of the tip. Corresponding data for source-drain voltages of up to $2\mathrm{mV}$ can be found in Appendix pp4. (a) Raw data. (b) $\mathrm{\Delta }G\left(V_{\mathrm{cav}}\right)=G\left(V_{\mathrm{cav}}\right)-〈G\left(V_{\mathrm{cav}}\right)〉$ for small steps in $V_{\mathrm{sd},\mathrm{dc}}$, where $〈G\left(V_{\mathrm{cav}}\right)〉$ is the average conductance in $V_{\mathrm{cav}}$ at fixed $V_{\mathrm{sd},\mathrm{dc}}$. The conductance at zero dc bias ($V_{\mathrm{sd},\mathrm{dc}}=0\mathrm{mV}$) is denoted in red and the lines are offset with respect to each other.

Figure 4

(a) Conductance quantization of the quantum point contact in absence of the cavity. The blue arrow marks the QPC voltage $V_{\mathrm{qpc}}$ at which the trace in (b) is taken. (b) Conductance through the cavity as a function of the cavity gate voltage for the QPC voltage marked by the blue arrow in (a) (third conductance plateau). The dashed line marks the pinch-off voltage of the cavity gate.

Figure 5

Differential conductance $G(x,V_{\mathrm{sd},\mathrm{dc}})$ for a strongly invasive tip potential ($V_{\mathrm{tip}}=-6\mathrm{V}$) along a similar line as the red dashed line in Fig. 1. (a) Raw data. (b) Conductance difference $\mathrm{\Delta }G\left(x\right)$ for tip positions $x$ along the red line in (a) and small steps in $V_{\mathrm{sd},\mathrm{dc}}$. The red curve corresponds to zero source-drain bias and the lines are offset with respect to each other. Black dashed guides to the eye denote three exemplary minimum-to-maximum transitions.

Figure 6

Conductance difference $\mathrm{\Delta }G(x,V_{\mathrm{sd},\mathrm{dc}})$ of the data depicted in Fig. 2.

Figure 7

Differential conductance $G(V_{\mathrm{cav}},V_{\mathrm{sd},\mathrm{dc}})$ depicted in Fig. 3 for a larger range of $V_{\mathrm{sd},\mathrm{dc}}$.

Figure 8

Conductance difference $\mathrm{\Delta }G\left(V_{\mathrm{sd},\mathrm{dc}}\right)$ for small steps in the tip positions $x$ along the red line in Fig. 2.