Electronic Structure: Impurity and Defect States in Metals and Alloys

Abstract

The equation for the Green?s function that describes the propagation of an electron in a solid is derived. After obtaining the Green?s function for a perfectly periodic solid, the modifications required to describe a single embedded impurity are derived. The most successful approximation to the average Green’s function for a substitutional alloy, the coherent potential approximation (CPA), is derived. A very powerful method for calculating the electronic states of any structure of atoms, either ordered or disordered, is the locally self-consistent multiple-scattering (LSMS) method. This order-N method for calculating the Green?s function is described. LSMS calculations on substitutional alloys are used to illustrate the limitations of the CPA. A hybrid of the LSMS and the CPA, the polymorphous CPA (PCPA), gets around these limitations. Applications of the PCPA are described. Finally, other extensions of the CPA and other Green?s function methods are explained.