Self-consistent localization theory in magnetic fields and the upper critical field of disordered superconductors

Abstract

The authors revisit the theory of the upper critical field of disordered superconductors and present an alternative calculation of Bc2 where they avoid semiclassical arguments and work from the start with Landau levels. As in other current theories they neglect Coulomb interactions and concentrate on localization effects. by generalizing the self-consistent theory by Vollhardt and Wolfle (1980) to a system lacking translational and time reversal invariance. They analyse the theory in configuration space and discuss the approximations that lead to closed self-consistent equations that would reproduce well known results in the non-magnetic case. In the low-field limit they obtain a pair of coupled equations for the frequency-renormalized diffusion coefficient and conductivity. As a result of detailed calculation from first principles they detect a suppression of the diffusion pole in one of the equations that was overlooked in a phenomenological theory. The results for the upper critical field exhibit a change from negative to positive curvature in the Bc2 versus T plot for increasing disorder and they are compared with those obtained in the theory of Kotliar and Kapitulnik (1986).