Superconductivity and Localization in Disordered Systems: A Local Gauge Invariant Approach

A new tight binding theory for superconductivity in disordered systems is constructed on the basis of local gauge invariant n orbital models. The large n limit realizes and justifies BCS type results for weak coupling and arbitrarily narrow bands as exact solutions including modifications from the variable density of states. The 1/ n expansion provides a systematic treatment of superconducting-, localization-, and magnetic fluctuations and of Coulomb repulsion. As first applications we derive i) deviations from Anderson's theorem due to the density of states variation and ii) logarithmic reduction of the critical concentration of magnetic impurities due to localization in 2D systems and critical reduction of T c in 3D due to critically decreased spinflip lifetime near the mobility edge (diffusion localization). A similar effect is found for the upper critical magnetic field and is compared with recent theories of Fukuyama and Maekawa et al.