Interplay between the Anderson model of localization and BCS superconductivity: The finite band width transition

Abstract

We combine the tight binding Anderson model of disorder with a mean field BCS interaction. The transition temperature is obtained as a general relation which depends on the disorder averaged spectral density associated with the electron propagator between neighboring lattice sites. This relation is obtained using the locator expansion technique. As a main result we predict superconductivity in the disorder induced localized state. There is a maximum bandwidth where superconductivity is destroyed. This is consequence of the local pairing assumed in the model.