Theory of Dirty Superconductors in Weakly Localized Regime

Abstract

The superconducting transition temperature Tc and upper critical field Hc2 in dirty superconductors are studied by taking into account the dynamically screened Coulomb interaction and disorder,perturbatively.We find that the results depend on the relative magnitude of tq 1 and coD,t0 and coD being the relaxation time of an electron and the phonon-Debye frequency,respectively,even in the weakly localized regime. We examine the case of t0-1 and wD exclusively in this paper. The Anderson localization enhances the Coulomb repulsion between electrons and modifies the density of states. In addition, disorder induces the depairing effect due to the retardation of the Coulomb interaction. We obtain that Tc decreases in proportion to the sheet resistance in thin films and to l2 in bulk systems where l=h/2pet0,eF being the Fermi energy. The correction in Tc is a function of | In Tct0| in both bulk systems and thin films. © 1984, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.