Superconductor-insulator transitions in films and bulk materials

Two different approaches to the problem of the superconductor-insulator transition in two-dimensional (2D) and three-dimensional (3D) systems are discussed. In the first approach, the mean field theory of the superconducting transition is modified to include the electron-electron repulsion and disorder. In the alternative phenomenological approach, the critical region around the quantum phase transition is treated in terms of interacting bosons. In our point of view, these two methods are applicable respectively in the two complimentary regimes of weak and strong quantum fluctuations of the order parameter. The combination of the two approaches allows us to explain the observed recently non-monotonous dependence of the resistivity on magnetic field in 3D strongly disordered superconductors. It also allows us to relate the non-monotonous temperature dependence of the resistivity in the 2D case to the crossover between the two regimes. The non-monotonous behavior of the resistivity near the quantum phase transitions in the 2D and 3D cases is explained by the suppression of superconductivity with the increase of temperature or magnetic field, which at even higher temperatures or fields is followed by the suppression of localization. Matching of the results of the two approaches yields also the width of the critical region for the quantum phase transition.