Anderson localization and the theory of dirty superconductors. II

We study the interplay between Anderson localization and superconductivity. We incorporate the scale dependence of the diffusion constant in the evaluation of the Landau-Ginzburg functional. The zero-temperature coherence length is strongly reduced and it saturates when it crosses over with a thermal length $l_T$=[2πT(dn/dμ${\left)\right]}^{\mathrm{-}1/d}$ which emerges from the theory. In this regime the Ginzburg criterion predicts a critical region of order unity where thermodynamic fluctuations are important. On the insulating side of the mobility edge the coherence length becomes equal to the localization length and the size of the critical region is very large. We study in detail the upper critical fields and discuss the conditions for the appearance of positive curvature in the $H_{c2}$ versus T plot.