Theory of surface electronic states in metallic superlattices

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Abstract
We report the existence of surface-localized electronic states for a superlattice consisting of alternating slabs (parallel to the surface) of two different metals. The superlattice has a larger periodicity in the direction perpendicular to the slabs and therefore many electronic branches in the folded Brillouin zone. In the gaps existing between these bulk branches appear the surface-localized modes. The theory is developed on an s-band model of a simple-cubic crystal. The simplicity of this model allows one to obtain in closed form the bulk and (001) surface Green’s functions for this superlattice. The analytic knowledge of these functions enables us to study easily all the bulk and surface electronic properties of this metallic superlattice, which otherwise would require huge numerical calculations. We give here the analytic expression we obtained for the folded bulk electronic bands and also the expression that gives the surface electronic states. A few figures for specific cases illustrate these results.