Analytic properties and accuracy of the generalized Blackman-Esterling-Berk coherent-potential approximation

The Blackman-Esterling-Berk (BEB) theory, generalized to nonorthogonal basis sets and complicated elementary cells [K. Koepernik, B. Velicky, R Hayn, and H. Eschrig, Phys. Rev. B 55, 5717 (1997)], is inspected in great detail with respect to its analytic properties and numerical accuracy. We give a proof of the single impurity limit fulfilled by BEB theory, thus clarifying some critical points in the derivation of the theory. We undertake extensive numerical tests for the BEB coherent-potential approximation (CPA) to check the range of applicability of the included single-site approximation. The BEB CPA turns out to give good results in a wide range of energy parameters.