Generalization of the coherent-potential approximation to compositionally modulated alloys

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Abstract
We propose a generalization of the coherent-potential approximation (CPA) in order to make it applicable to compositionally modulated alloys. This generalization (MODCPA) preserves all the desirable properties of CPA, such as analyticity and ease of computation, and in many cases yields results which are much more accurate than those obtained within the original CPA. Numerical calculations for the cases of one-dimensional and three-dimensional tight-binding model systems reveal that composition modulation may produce increased structure in the density of states with the setting in of energy gaps for certain directions and strengths of modulation. We found that the original CPA is not capable of accounting for such effects of the modulation. On the other hand, modulation effects on the density of states are quite accurately described within the MODCPA. Finally, we also show how the MODCPA can be extended to a cluster theory and how it can be applied to alloys describable to tight-binding Hamiltonians with both diagonal and off-diagonal disorder, and to alloys describable by muffin-tin Hamiltonians.