Augmented-plane-wave approach to scattering of Bloch electrons by an interface

Abstract

A full-potential augmented-plane-wave-based variational method is proposed to construct the scattering wave function for a system consisting of two semi-infinite crystals separated by an interface region. The two half spaces are represented by their complex band structures, and a basis set expansion is used to represent the wave function in the embedded region. The method is based on solving the equation $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\gamma}}(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}\ensuremath{-}E)\ensuremath{\Psi}=0$ in the scattering region, which is equivalent to the original Schr\"odinger equation, and the presence of the operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\gamma}}$ makes it possible to formulate the variational problem in terms of plane waves. Current conservation considerations are drawn on to include the requirement of the smooth continuity of the wave function into the variational functional. The problem of the overcompleteness of embedding basis sets is discussed and a solution is presented. The method is verified by calculating the electron diffraction and surface states on (100) and (111) surfaces of Al and Cu. The accuracy and convergence properties of the computational scheme are analyzed.