THEORY OF ELECTRONIC TRANSPORT IN DISORDERED BINARY ALLOYS - COHERENT-POTENTIAL APPROXIMATION

The coherent-potential approximation (CPA) for single-particle properties of electrons in a disordered alloy AxB1-x (Soven and others) is extended to complex admittances. The one-electron Kubo formula is used. The CPA is viewed as a single-site decoupling of the averaged multiple-scattering expansion. It properly gives the exact formulas in the limits of weak scattering (Edwards) and of dilute alloys (Langer). For any x and any random-potential strength, CPA satisfies a number of physical conditions, including energy and particle-number conservation. The CPA equations are exactly soluble for a single-band model with short-ranged random scatterers. The vertex corrections are related to the response of local densities to a given disturbance. For the electrical conductivity σ, they vanish. Variation of σ with the randompotential strength is studied numerically. A low-mobility region appears well before the band splits. In the split-band limit, CPA yields a reasonable finite σ in the host band, but it fails in the impurity band. © 1969 The American Physical Society.