Scattering of electronic waves in square and triangular lattice half-planes with monoatomic step

TL;DR

This paper presents an exact analytical solution for electronic wave scattering in square and triangular lattice half-planes with a step, using the Wiener-Hopf method, and compares it with numerical results.

Contribution

It introduces an exact solution approach for surface scattering problems in lattice structures using the discrete Wiener-Hopf method.

Findings

Exact solution for scattering problem derived

Far-field approximation matches numerical results

Applications to surface energy bands in crystals

Abstract

Scattering of electronic waves in square and triangular lattice half-planes by a step on the surface is analyzed using the nearest-neighbour tight binding approximation. The changes in lattice spacing and the transfer integral between nearest-neighbor sites near the surface are ignored. A standard application of the discrete Wiener-Hopf method leads to an exact solution of the scattering problem associated with incidence from the `bulk'. A far-field approximation of electronic wavefunction, as well as its graphical comparison with a numerical solution, are also provided. Natural applications and possible extensions are based on the bulk Brillouin zone for two dimensional lattice planes as well as surface energy bands for fcc crystals.