Collective Modes and Ground State Energy of the Semi-infinite Electron Gas

Abstract

The RPA linear response theory as applied to the semi-infinite electron gas, in particular the infinite barrier model, is discussed in terms of the normal mode charge density fluctuations of the system. The normal modes separate into a discrete, surface mode with an electric field extending outside the solid and a continuum of bulk modes with no such fields. The surface mode, which corresponds to the undamped surface plasmon in the longwavelength limit, is examined at wave vectors up to the plasmon cut-off where it merges with the bulk modes. The bulk modes are also affected by the surface and we have calculated their phase shifts as a function ofx, the wave vector perpendicular to the surface. In terms of these phase shifts we then discuss the change in the number of bulk modes when a surface is created; about 1/4 of a bulk mode is removed over an interval close tox=0 in addition to another 1/4 removed discretely atx=0. The surface exchange-correlation energy can be split into the change in the zero-point energy of the plasmons and the contribution from the screened electron-hole pair excitations, and we discuss the contribution in terms of zero-point energy of the surface plasmon and the change in the number of bulk modes.