Cluster generalization of the coherent-potential approximation on the basis of the projection formalism in an augmented space

The electron spectrum of a binary alloy in the tight-binding model with diagonal disorder is considered. The formalism of an augmented space is used in conjunction with memory functions, and the averaged resolvent is represented as an operator continued fraction. A general scheme is proposed for constructing self-consistent approximations, including the coherent-potential approximation and the traveling-cluster approximation. It is shown that the self-consistent approximations obtained in the general case for the averaged resolvent have the correct analytic properties.