FREQUENCY-DEPENDENCE OF THE ADMITTANCE OF A QUANTUM POINT-CONTACT

Using a Boltzmann-like kinetic equation derived in the semiclassical a pproximation for the partial Wigner distribution function, we determin e the ac admittance of a two-dimensional quantum point contact (QPC) f or applied ac fields in the frequency range omega approximate to 0-50 GHz. We solve self-consistently an integral equation for the spatial d istribution of the potential inside the QPC, taking into account the t urning points of the semiclassical trajectories. The admittance of the QPC is a strong function of the gate voltage. This gate voltage can b e used to ''tune'' the number of open channels (N) for electron transp ort. 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 i nductive character, because of the predominant role of the open channe ls. In contrast, for N=0 or 1, for most values of the gate voltage, th e imaginary Dart of the admittance is negative, corresponding to capac itive behavior. For gate voltages near values at which channels open o r close, very strong nonlinear effects arise, and the admittance oscil lates rapidly (with its imaginary part sometimes changing sign) both a s the function of gate voltage (at fixed frequency) and as a function of frequency (at fixed gate voltage). Experimental observation of thes e oscillations would provide an important test of our semiclassical ap proach to the ac response of a QPC. We explore the low-frequency regim e and investigate the extent to which one can understand the admittanc e in terms of a static conductance and a ''quantum capacitance'' and a ''quantum inductance.'' We show that it is possible to choose the gat e 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'' c oncepts. We study how this approach breaks down at higher frequencies, where strongly nonlinear behavior of the admittance arises. We estima te the value of frequency, omega(c), at which the crossover from the l ow-frequency linear regime to the high-frequency nonlinear behavior oc curs. For chosen parameters of a QPC, omega(c) approximate to 10 GHz. [S0163-1829(98)02339-X].