Generalized coherent-potential method for disordered systems

A tractable way to generalize the coherent-potential method beyond the coherent-potential approximation (CPA) is presented. Explicit expressions are derived for a single-band tight-binding-approximation model including the correlations between first nearest neighbors. The potential change when one atom type is replaced by another at a given site is assumed to extend beyond that site so as to satisfy perfect shielding and include hopping-term variations. By considering the restrictions imposed by perfect shielding throughout the whole concentration range, two more conditions on the potential are found in addition to that corresponding to the Friedel sum rule. It is shown how to modify the CPA so as to satisfy perfect shielding. The main effect of this modification is to rigidly shift the CPA density-of-states curve so as to maintain the Fermi energy fixed for all concentrations. The modified CPA is limited in the possible number of physical alloys that it can hope to accurately describe. When the hopping perturbation is large, correlations between first neighbors are important and the CPA is not adequate.