The Hall conductivity of a disordered alloy in the coherent-potential approximation

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Abstract
The Hall conductivity is formulated within the CPA for the tight-binding model Hamiltonian. Particular care is taken for gauge invariance of the formulation. The present formalism is applicable to the case with off-diagonal disorder in addition to diagonal disorder, and the effect of the off-diagonal disorder on the Hall conductivity is investigated for the model considered by Shiba (1971) and that by Blackman et al. (1971). It is shown that the vertex correction to the Hall conductivity vanishes for these models provided that the lattice has the inversion symmetry. For a numerical application of the present formalism a binary alloy with a simple cubic lattice is investigated.

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