Superconductor-insulator transitions: Phase diagram and magnetoresistance

The influence of the disorder-induced Anderson localization and electron-electron interaction on the superconductivity in two-dimensional systems is explored. We determine the superconducting transition temperature T-c, the temperature dependence of the resistivity, the phase diagram, and the magnetoresistance. The analysis is based on the renormalization group (RG) for a nonlinear sigma model. The derived RG equations are valid to the lowest order in disorder but for an arbitrary electron-electron interaction strength in a particle-hole and the Cooper channels. Systems with preserved and broken spin-rotational symmetry are considered, with both short-range and long-range (Coulomb) interactions. In the case of short-range interaction, we identify parameter regions where the superconductivity is enhanced by localization effects. Our RG analysis indicates that the superconductor-insulator transition is controlled by a fixed point with a resistivity R-c of the order of the quantum resistance R-q = h/4e(2). When a transverse magnetic field is applied, we find a strong nonmonotonous magnetoresistance for temperatures below T-c.