Abstract

We study the influence of disorder on the temperature of superconducting transition within the sigma-model renormalization-group framework. Electron-electron interaction in particle-hole and Cooper channels is taken into account and assumed to be short range. The approach takes into account mutual renormalization of disorder and all interaction constants (that, in particular, leads to mixing of different interaction channels). Two-dimensional systems in the weak localization and antilocalization regime, as well as systems near mobility edge are considered. We demonstrate that in all these regimes Anderson localization leads to strong enhancement of the critical temperature related to the multifractality of wave functions. Screening of the long-range Coulomb interaction thus opens a promising direction for searching novel materials for high-temperature superconductivity.