Long Jumps in Surface Diffusion: A Microscopic Derivation of the Jump Frequencies

Starting from a microscopic Hamiltonian for a particle on the corrugated surface of a solid we derive the master equation for phonon-mediated hopping and friction using the Wannier representation. For a sinusoidal corrugation (in addition to a Morse surface potential) we investigate the role of interband transitions and numerically calculate transition probabilities. We find that long hops beyond nearest neighbor sites are significant, particularly for weakly coupled systems.