Anderson Localization and Energy Gap in Two-Dimensional Superconductors

Abstract
Effects of the Anderson localization on energy gap Δ in two-dimensional dirty superconductors are investigated theoretically. It is shown that Δ is suppressed by the interplay of the Coulomb repulsive interaction and impurity scattering. However, as far as the impurity scattering is weak, it is proved definitely that Δ remains to be finite at any temperature below the transition temperature, that is, the superconductivity is always stable against the Anderson localization.