Dispersion of longitudinal plasmons for a quasi-two-dimensional electron gas

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Abstract
Confinement of electrons in ultrathin metallic films leads to subbands. By increasing the thickness of the electron layer, the subbands will dissolve into a quasicontinuum, with the number of electrons per unit volume kept constant. Within the random-phase approximation, the two-dimensional plasmon, which originally follows Stern’s dispersion relation, becomes a longitudinal surface plasmon. The plasmon excitations of a model metallic film are investigated by including all subbands. Single-particle excitations, which exhibit the depolarization shift, converge into the plasma excitation spectrum. With further increases in the film thickness, the bulk plasmon arises and the surface plasmon remains. Our analysis shows how quantum size effects evolve into hydrodynamical classical size effects with increasing thickness of the film.