Linear response of a semi-infinite substrate with a two-dimensional conductive surface layer in the plasma-pole approximation

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Abstract
The current-current linear-response function for a semi-infinite compressible electron-gas substrate with a surface layer of zero thickness is evaluated by treating the substrate hydrodynamically. No assumptions are made regarding the current-current response of the surface layer, and retardation effects are fully included. Contact is made with Nakayama's paper on surface plasmons, and a discussion of the effects of a finite compressibility of the background electron gas on the surface modes is included. Angular distributions for Raman scattering by a simple type of surface plasmon are calculated as an application of these results.