Superconductor-insulator transitions: Phase diagram and magnetoresistance
Abstract
Influence of disorder-induced Anderson localization and of electron-electron interaction on superconductivity in two-dimensional systems is explored. We determine the superconducting transition temperature Tc, the temperature dependence of the resistivity, the phase diagram, as well as the magnetoresistance. The analysis is based on the renormalization group (RG) for a nonlinear sigma model. Derived RG equations are valid to the lowest order in disorder but for arbitrary electron-electron interaction strength in particle-hole and Cooper channels. Systems with preserved and broken spin-rotational symmetry are considered, both with short-range and with long-range (Coulomb) interaction. In the cases 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 Rc of the order of the quantum resistance Rq = h/ 4e2. When a transverse magnetic field is applied, we find a strong nonmonotonous magnetoresistance for temperatures below Tc.