3.1.2.3.1 Theoretical studies on image states

This chapter discusses surface states and image states of metals. An analysis of experimental results on image-potential-induced surface states is presented. Plasmon dispersion and single-particle effects in the medium response are included as well as the bound-state nature of an electron creating its own image potential. The formalism is accurate enough to explain well the existing experimental binding energy data. A peak width narrower than the experimental one is predicted. Density-functional theory is applied to calculate image-potential states at metal surfaces with different electron densities. The surface potential, obtained from a self-consistent quantum mechanical calculation based on the jellium model, yields the correct long-range image potential, since non-local exchange-correlation energy functional is used. The many-body effects lead to drastic changes in the energies of the Rydberg states n = 1, 2 both at high and low electron densities. Effective potential at jellium surfaces is illustrated. The binding energy of surface states is a multibranch function of an image-plane position. The states of the Rydberg series (including the conventional crystal-derived states) have a unique labeling in terms of the number of extrema in wave function beyond a crystal edge, and the spatial extent of the image states is determined by their binding energy. Half-widths for the first image states of Ag and Cu (111) faces as a function of wave-function penetration into the crystal are tabulated.