Hydrodynamic model for surface plasmons in metals and degenerate semiconductors

A hydrodynamic model is used to study the effect of the electron-density profile at the surface on surface-plasmon modes. The model consists of an extension of Bloch's original hydrodynamic model to study an inhomogeneous electron gas capable of self-oscillations about a ground state given by the Hohenberg-Kohn-Sham theory of the inhomogeneous electron system. We write down an expression for the conductivity tensor which formally contains all relevant information within the context of our hydrodynamic formulation. The qualitative features of the model are illustrated by detailed numerical calculations for smooth electron-density profiles. The dispersion relation of both regular surface-plasmon and higher-multipole excitations (which occur for sufficiently diffuse profiles) are studied for a wide range of wave vectors from the optical ($\omega \sim \mathrm{cq}$) to the nonretarded or electrostatic limit.