Improvements of the Coherent Potential Approximation for the Random Lattice Problems

概要

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The perturbation term of the one-particle Green's function of an electron in a random lattice is expressed as a sum of terms related with one site, two sites, three sites, and so on. The coherent potential approximation is rederived under the assumption that the sum of the terms related with two or more sites can be ignored if the unperturbed Hamiltonian is chosen in such a way that the sum of the one-site terms is put equal to zero. The next approximation is obtained by assuming that the sum of the terms related with the clusters of sites other than the one sites and the nearest neighbor pairs of sites can be ignored, when the unperturbed Hamiltonian is so chosen that the sum of the terms related with a one site or a nearest nighbor pair of sites is put equal to zero. This approximation is applicable to the random alloy problems where the diagonal as well as off-diagonal randomness exist. If the randomness is restricted only to the diagonal one, the approximation is equivalent to the one proposed by Cyrot-Lackmann and Ducastelle (Phys. Rev. Letters 27 (1971) 429) and by Nickel and Krumhansl (Phys. Letters 36A (1971) 111). Systematic improvements of the approximations are suggested.
社団法人日本物理学会の論文
1973-05-05