Real-space solution of the coherent potential approximation equations in the Shiba approximation

Abstract

We present a generalization of a real-space method for solving the self-consistent field equations of the coherent potential approximation (CPA) for the case of multiplicative off-diagonal disorder originally proposed by Shiba. This generalization allows us to account for the difference in the bandwidths of the alloy-pure components in the study of the electronic properties of disordered alloys. The coherent potential and the Green function of the effective medium are expanded as continued fractions. It is shown that, contrary to the standard CPA method, the effective Hamiltonian is energy independent but acts in an augmented space, so that the recursion technique is directly applicable. This real-space approach opens up the possibility of studying the electronic structure properties of both chemically and topologically disordered alloys. Applications to the calculation of the density of states as well as to the study of stability of models and more realistic tight-binding Hamiltonians for binary transition-metal alloys are discussed.