ac response of quantum point contacts with a split-gate configuration

The alternating-current response of a quantum point contact (QPC) is numerically investigated using the nonequilibrium Green function method combined with an effective mass theory. We found that the susceptance of a QPC increases stepwise with increasing gate voltage, when the width of the quantization plateau in the gate voltage-conductance curve is narrower than the width of the region where the conductance changes gradually. We also show that the height of a susceptance step is proportional to the ac-bias frequency. These simulation results are in excellent qualitative agreement with recent experimental results. Moreover, we found that the transition from capacitive susceptance to inductive susceptance occurs with increasing gate voltage. The capacitive-inductive transition point is independent of the ac-bias frequency, but it does depend on the contact width.

Figure 1

(a) Confinement potential of a QPC with a length $L_x=30a$ and a width $L_y=30a$ with $a=2.5$ nm. The arrow shows the direction of the electron flow. (b) Confinement potential profile for $-e{V}_b/E_F=0.5$ and $\Delta =L_y/4$. The solid curves represent the potentials at $x/a=0$, $\pm 5$, and $\pm 10$ as a function of $y$.

Figure 2

(a) Conductance and (b) susceptance of a QPC as a function of the height of the potential barrier induced by the gate voltage $V_b$. The solid, dotted, and dashed curves correspond to ac-bias frequencies of $\nu =100$, 200, and 300 MHz, respectively. Open squares in (a) denote the dc conductance. The inset shows the ac-bias frequency dependence of the susceptance for susceptance steps of $V_b=10$ mV (circles) and $-10$ mV (triangles). The step edge height is proportional to the ac-bias frequency in the low-frequency regime that is shown in the inset.

Figure 3

(a) Conductance and (b) susceptance of a QPC with $\Delta =L_y/4$ (solid curve), $L_y/5$ (dotted curve), and $L_y/6$ (dashed curve) as a function of the gate voltage. Here, the ac-bias frequency is fixed at $\nu =300$ MHz.

Figure 4

Dependence of the gate voltage on (a) the conductance and (b) susceptance of the QPC with $L_x=30a$ (solid curve) and $L_x=50a$ (dotted curve). Here, the ac-bias frequency and the potential curvature are fixed at $\nu =300$ MHz and $\Delta =L_y/6$, respectively. The left and right axes in (b) are shown on the susceptance in the case of $L_x=30a$ and of $L_x=50a$.