AC TRANSPORT AND COLLECTIVE EXCITATIONS IN A QUANTUM POINT-CONTACT

We study the a.c. transport through a two-dimensional quantum point co ntact (QPC) using a Boltzmann-like kinetic equation derived for the pa rtial Wigner distribution function. An integral equation for a potenti al inside a QPC is solved numerically. It is shown that the electric f ield inside a QPC is an inhomogeneous function of the spatial coordina te, with a characteristic scale equal to the distance between the elec tron's turning points. A dependence of the admittance on the frequency of the a.c. field is found in the frequency range, omega approximate to 0-50 GHz. The contribution to the imaginary part of the admittance due to the open and closed channels is numerically calculated. It is s hown that the crossover of quantum capacitance and quantum inductance from localized behaviour to distributed behaviour takes place at omega similar to 10 GHz. A transition from 2D plasmons to quasi-1D plasmons is analysed as a function of two dimensionless parameters: k(x)d(0) ( where k(x) is the longitudinal wavevector and do is the width of the Q PC) and the number of open electron channels, N.