Superconductor-insulator transitions: Phase diagram and magnetoresistance

TL;DR

This paper investigates how disorder and electron interactions influence superconductivity in two-dimensional systems, analyzing phase diagrams, resistivity, and magnetoresistance using renormalization group methods.

Contribution

It provides a comprehensive RG-based analysis of the superconductor-insulator transition considering various interaction types and symmetries, identifying conditions that enhance superconductivity.

Findings

Superconductivity can be enhanced by localization effects in certain parameter regimes.

The superconductor-insulator transition is governed by a fixed point with resistivity near the quantum resistance.

A strong nonmonotonous magnetoresistance occurs below the critical temperature when a magnetic field is applied.

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 $T_c$, 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 $R_c$ 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 $T_c$.