The inverse dielectric function of a quasi-two-dimensional electron gas in a quantum well: plasmons in a thin metal layer

Abstract

A formal expression for the energy-loss function of a fast electron interacting with an inhomogeneous quasi-2D electron gas in a quantum well is given in the quasiclassical approximation. It uses the non-local inverse dielectric function derived in a previous paper. As an illustrative example, the plasmon dispersion relations of a thin metal film embedded in dielectric caps are calculated, taking into consideration the influence of the empty part of the electronic spectrum, the dielectric discontinuity of the system and the influence of various occupied subbands. By following the peaks of the loss function, rather than seeking zeros of the secular determinant, one can easily obtain the plasmon branches even when these enter the domains of Landau damping. For several occupied subbands the number of acoustic plasmon branches is the same as the number of occupied subbands, and the intersubband plasmon branches at q = 0 appear at energies close to each one of the transitions allowed in the system, which we call the leading transition of the plasmon branch. The depolarization effect is shown to be strongly dependent on the population of the system and on the type of the leading transition involved, i.e. a leading transition between occupied subbands or between one occupied and one empty subband. Some regularities for this effect are observed, correlating the depolarization energy with the order of the states involved as the leading transition of the plasmon mode.