Relativistic and non-relativistic electron transport in disordered alloys I. Theory

The electrical conductivity of disordered alloys is calculated using the Korringa-Kohn-Rostoker-coherent-potential approximation alloy theory in conjunction with the local approximation to density functional theory and the Kubo-Greenwood equation. Relativistic and non-relativistic expressions for the conductivity are derived. A technique for evaluation of the Kubo-Greenwood equation for arbitrary crystal symmetry using group-theoretical methods is described. Explicit expressions for scattering and current operators at complex energies below the real axis which occur in the evaluation of the Kubo-Greenwood equation are given.