Surface scattering on topological networks

Abstract

The quantum mechanical network model of electrons in solids as introduced by Montroll is used to construct a multiple-scattering formalism for scattering in slightly aperiodic lattices. We examine both the case of Bloch electron scattering and diffractive scattering (as applied to LEED) from surfaces. In the former case the resulting equations are completely analogous to those derived by Koster and Maradudin in their analyses of the scattering of electron and lattice waves by defects. In the latter case the differential cross section functionally resembles Fraunhofer diffraction in optical systems, and is explicitly dependent upon the atomic geometry and the atomic potentials of the surface. All computations are analytic. Since qualitative agreement with experiment is excellent, our results seem to imply that the geometric structure of a material dominates the electronic character of a scattering system.