Theory of Upper Critical Fields in Highly Disordered Superconductors: Localization Effects

The authors compute the temperature $T$ dependence of the upper critical field $H_{c^2}$ arising from incipient localization effects in highly disordered three-dimensional superconductors. In agreement with experiments, $H_{c^2}\mathrm{}\left(T\right)\mathrm{}$ is enhanced over the standard result for dirty superconductors. This enhancement is due to the field-induced suppression of localization. It is demonstrated that properties of $H_{c^2}\mathrm{}\left(T\right)\mathrm{}$ are intimately connected to those of the magnetoresistance. This connection and other predictions of the authors' theory can be tested experimentally.