Dynamic Image Potential at an Al(111) Surface

Abstract

We evaluate the electronic self-energy $\ensuremath{\Sigma}(E)$ at an Al(111) surface using the $\mathrm{GW}$ space-time method. This self-energy automatically includes the image potential ${V}_{\mathrm{im}}$ not present in any local-density approximation for exchange and correlation. We solve the energy-dependent quasiparticle equations and calculate the effective local potential experienced by electrons in the near-surface region. The relative contribution of exchange proves to be very different for states above the Fermi level. The image-plane position for interacting electrons is closer to the surface than for the purely electrostatic effects felt by test charges, and, like its classical counterpart, is drawn inwards by the effects of atomic structure.