Charge Rearrangement and Screening in a Quantum Point Contact

Compressibility measurements are performed on a quantum point contact (QPC). Screening due to mobile charges in the QPC is measured quantitatively, using a second point contact. These measurements are performed from pinch-off through the opening of the first few modes in the QPC. While the measured signal closely matches a Thomas-Fermi-Poisson prediction, deviations from the classical behavior are apparent near the openings of the different modes. Density functional calculations attribute the deviations to a combination of a diverging density of states at the opening of each one-dimensional mode and exchange interaction, which is strongest for the first mode.

Figure 1

Linear (a) and nonlinear (b) conductance of the device sketched in inset of (a). Plateaux fall below $G_0$ due to finite series resistance, not subtracted off in figures. (b) Characteristic signatures [9] of the 0.7 structure are observed: high-bias plateau near $0.8(2e^2/h)$ (dashed ellipse) and zero-bias anomaly (solid ellipse). (c) Inset: Conductance of the detector QPC, used to derive the mapping $V_{\mathrm{eff}}(V_{\mathrm{QPC}})$. Optimal working range of the detector indicated by dotted ellipse. Main panel: Fourteen charge sensing measurements covering a wide range of $V_{\mathrm{QPC}}$. Left axis: Detector conductance $G_{\det }$. Right axis: $V_{\mathrm{eff}}$ mapped from $V_{\mathrm{QPC}}$ as described in text. (d) Conductance trace of the QPC (right axis) and derivative $D\equiv d{V}_{\mathrm{eff}}/d{V}_{\mathrm{QPC}}$ of the detector data (left axis) for identical gate settings. $D$ is a measure of screening of electric fields by the QPC. Dashed lines mark steep rises in the conductance of the QPC, coinciding with suppressions in $D$ which indicate enhanced screening.

Figure 2

(a) $D^{\mathrm{SETE}}\equiv d{V}_{\mathrm{eff}}/d{V}_{\mathrm{QPC}}$ extracted from numerical simulation of the device. The red dashed lines are guides to the eye, showing linearity of $D^{\mathrm{SETE}}$ around pinch-off. No modulation can be observed in the simulation, which does not account for the one-dimensional nature of the QPC [18]. (b) The shaded area indicates a pronounced dip of $D$ around pinch-off. No such feature is observed in the simulated $D^{\mathrm{SETE}}$. (c) $D^{\mathrm{DFT}}$, as calculated from DFT simulation of a modified QPC (inset) with a detector 200 nm beneath the plane of the QPC. Thick solid line, LDA with actual GaAs effective mass; dashed line, LDA with doubled mass; dotted line, Hartree approximation with actual mass. The thin solid line shows the conductance of the QPC in the LDA approximation (right-hand scale). The dashed red line is again a guide to the eye, showing the change in slope of the detector signal at pinch-off within all these simulations. The simulations dip below this guide line at the opening of each new mode. Within the Hartree approximation the dips are all roughly equal in size, but in LDA the dip at pinch-off is substantially larger than the others, as observed in experiment.

Figure 3

Curves from Fig. 2c expanded and shifted vertically to highlight subtle differences among the approximations at the opening of the first and second subbands. The LSDA curve with an additional dip associated with spin rearrangement is also shown, unshifted with respect to the LDA curve.