A.c. transport and collective excitation in a quantum point contact

Abstract

The authors calculate the a.c.-admittance of a two dimensional quantum point contact (QPC) using a Boltzmann-like kinetic equation derived for the partial Wigner distribution function. An integral equation for a potential inside a QPC is solved numerically. The dependence of the admittance on the frequency of the a.c. field is found in a wide frequency range {omega} {approx} 0--50 GHz. The contribution to the imaginary part of the admittance due to the quantum capacitance and inductance is numerically calculated. It is shown that the crossover from localized parameters--quantum capacitance and inductance--to distributed behavior takes place at {omega} {approximately} 10 GHz. A transition from 2D plasmons to quasi-1D plasmons is analyzed as a function of two dimensionless parameters: k{sub x}d{sub 0} (where k{sub x} is the longitudinal wave vector, and d{sub 0} is the width of the QPC), and the number of open electron channels, N.