ON THE ELECTRON SELF-ENERGY AT A METAL-SURFACE

On the basis of a full numerical calculation of the complex and non-local electron self-energy SIGMA(xc)(x, x'\E) in the GW approximation, we discuss the main qualitative features of the self-energy in the vicinity of a metal surface modelled by jellium. We find that Re SIGMA(xc) is negligible for \x - x'\ greater than a fraction of a Fermi wavelength, and that the general features of Re SIGMA(xc) are the same when moving from the bulk to the vacuum with most of its variation being in magnitude only. This behaviour is approximately reproduced with a purely local potential, namely V(xc)(x) of density functional theory, provided long-range correlations are taken into account. The same is not true for Im SIGMA(xc); its structure in the vacuum has a dominant non-local (\x - x'\ > lambda(F)) contribution. Thus, the use of a local function to describe damping at a metal surface is less well founded.