Theory of incomplete crystals, surfaces, defects, interfaces and layered structures

Abstract

This paper presents systematically the surface Green function matching analysis for systems with inherently discrete structure - e.g. phonons or tight-binding electrons. The general interface problem, the free surface, the vacancy - as a particular case of an inner surface - and point defects and adsorbates - as examples of interfaces - can all be treated on the same footing. By combining ideas of scattering and matching a unified approach encompasses a variety of different problems while yielding a method which can be used in practice for calculating e.g. surface, interface or defect state eigenvalues or spectral functions of interest. This holds for any type of physical states - electrons, phonons, waves - and for any chosen model. The practical combination with transfer matrix algorithms for planar geometry is discussed and an algorithm for growing shells is presented for point defects. Phonons allow for a discussion of the long-wave limit and contract is thus established with the surface Green function matching analysis for continuous media. The analysis is extended to layered structures - quantum wells and superlaticces - both for discrete and continuous systems.