Quantum transport theory in the coherent-potential approximation

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Abstract
A quantum formulation of the electrical conductivity of a disordered alloy is made in the coherent-potential approximation (CPA). The formalism is applicable to the case where the one-electron Hamiltonian (or its suitably renormalized form) depends additively on the configurations of individual sites. The configurational average of the vertex function which involves the random one-electron current operator is evaluated in the CPA by introducing the effective (or coherent) current operator, which is periodic but energy-dependent. It is shown that the case where the vertex correction to the vertex function vanishes is rather exceptional but that the kernel of the integral equation determining the vertex correction can be written in the separable type in the CPA. The correspondence between the present theory and the semiclassical Boltzmann theory is investigated in detail.