Superconductivity and Localization

Abstract

Abstract We present a review of theoretical and experimental works on the problem of mutual interplay of Anderson localization and superconductivity in strongly disordered systems. Superconductivity occurs close to the metal-insulator transition in some disordered systems such as amorphous metals, superconducting compounds disordered by fast neutron irradiation, etc. High-temperature superconductors are especially interesting from this point of view. Only bulk systems are considered in this review. The superconductor-insulator transition in purely two-dimensional disordered systems is not discussed. We start with a brief discussion of the modern aspects of localization theory including the basic concept of scaling, self-consistent theory and interaction effects. After that we analyze disorder effects on Cooper pairing and superconducting transition temperature as well as the Ginzburg-Landau equations for superconductors which are close to those for the Anderson transition. A necessary generalization of the usual theory of “dirty” superconductors is formulated which allows to analyze anomalies of the main superconducting properties close to the disorder-induced metal-insulator transition. Under very rigid conditions superconductivity may persist even in the localized phase (Anderson insulator). Strong disordering leads to considerable reduction of superconducting transition temperature Tc and to important anomalies in the behavior of the upper critical field Hc2. Fluctuation effects are also discussed. In the vicinity of the Anderson transition, inhomogeneous superconductivity appears due to statistical fluctuations of the local density of states. We briefly discuss a number of experiments demonstrating superconductivity close to the Anderson transition both in traditional and high-Tc superconductors. In traditional systems superconductivity is in most cases destroyed before the metal-insulator transition. In the case of high- Tc superconductors a number of anomalies show that superconductivity is apparently conserved in the localized phase before it is suppressed by a strong enough disorder.