Plasmons in simple metal slabs: a semi-classical approach

Collective excitations in simple metal systems can be successfully described in terms of a local one-body excitation operator Q, due to the long-range nature of the Coulomb interaction. For the plasmon modes of a simple metal slab, momentum expansions of Q are calculated using a variational procedure equivalent to a restricted RPA calculation. The dispersion relation and the density fluctuation for each mode are found in the sudden approximation using the proper Q operator and the RPA sum rule formalism. The contributions of the exchange and correlation energy are estimated using a local density functional. The positive background is described within a jellium model, while the ground-state electronic density is approximated by a double step profile. The density fluctuation of the plasmon modes above the plasma frequency form standing waves across the slab. The spectra below the plasma frequency are qualitatively different to those of local optics calculations due to the appearance of two multipole plasmon modes which shift the origin of the ω+ plasmon down. The dependence of the results on the width of the slab, the density of the simple metal and the surface diffuseness is discussed. The response of the slab to a q-dependent external excitation operator is analyzed. Throughout, the difference with to RPA and TDLDA calculations is stressed.