Frequency dependence of the admittance of a quantum point contact

Using a Boltzmann-like kinetic equation derived in the semiclassical approximation for the partial Wigner distribution function, we determine the ac admittance of a two-dimensional quantum point contact (QPC) for applied ac fields in the frequency range ω∼0 - 50GHz. We solve self-consistently an integral equation for the spatial distribution of the potential inside the QPC, taking into account the turning points of the semiclassical trajectories. The admittance of the QPC is a strong function of the gate voltage. This gate voltage can be used to 'tune' the number of open channels (N) for electron transport. We show that, for most values of gate voltage, the imaginary part of the total admittance is positive for N>1, so that the QPC has an inductive character, because of the predominant role of the open channels. In contrast, for N=0 or 1, for most values of the gate voltage, the imaginary part of the admittance is negative, corresponding to capacitive behavior. For gate voltages near values at which channels open or close, very strong nonlinear effects arise, and the admittance oscillates rapidly (with its imaginary part sometimes changing sign) both as the function of gate voltage (at fixed frequency) and as a function of frequency (at fixed gate voltage). Experimental observation of these oscillations would provide an important test of our semiclassical approach to the ac response of a QPC. We explore the low-frequency regime and investigate the extent to which one can understand the admittance in terms of a static conductance and a 'quantum capacitance' and a 'quantum inductance.' We show that it is possible to choose the gate voltage so that there is a large, low-frequency regime in which the admittance is well approximated by a linear function of frequency. In this regime, the admittance can be treated by 'equivalent circuit' concepts. We study how this approach breaks down at higher frequencies, where strongly nonlinear behavior of the admittance arises. We estimate the value of frequency, ωc, at which the crossover from the low-frequency linear regime to the high-frequency nonlinear behavior occurs. For chosen parameters of a QPC, ωc∼10GHz. copyright 1998 The American Physical Society