Self-consistent cluster CPA methods and the nested CPA theory

Abstract

The coherent potential approximation (CPA), is a useful tool to treat systems with disorder. Cluster theories have been proposed to go beyond the translation invariant single-site CPA approximation and include some short-range correlations. In this framework one can also treat simultaneously diagonal disorder (in the site-diagonal elements of the Hamiltonian) and non-diagonal disorder (in the bond energies). It proves difficult to obtain reasonable results, free of non-analyticities, for lattices of dimension higher than one ( D>1). We show electronic structure results obtained for a Hubbard model, treated in mean-field approximation, on a square lattice and a simple cubic lattice, with the simultaneous inclusion of diagonal and non-diagonal disorder. We compare the results obtained using three different methods to treat the problem: a self-consistent 2-site cluster CPA method, the Blackman–Esterling–Berk single-site like extension of the CPA and a nested CPA approach.