Random gauge models of the superconductor-insulator transition in two-dimensional disordered superconductors

TL;DR

This paper investigates the superconductor-insulator transition in two-dimensional disordered superconductors using four quantum rotor models, revealing universal critical behavior and conductivity consistent with experimental observations.

Contribution

It introduces and compares four gauge disorder models, demonstrating their universal critical behavior and conductivity at the transition.

Findings

Gauge and flux glass models share the same critical behavior.

Binary and Gaussian phase-glass models also exhibit similar critical properties.

Universal conductivity values are approximately the same across models and match experimental data.

Abstract

We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass and a Gaussian phase glass. The first two models, describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field while the last two describe the effects of random negative Josephson-junction couplings or $\pi$ junctions. Monte Carlo simulations in the path-integral representation of the models are used to determine the critical exponents and the universal conductivity at the quantum phase transition. The gauge and flux glass models display the same critical behavior, within the estimated numerical uncertainties. Similar agreement is found for the binary and Gaussian phase-glass models. Despite the different symmetries and disorder correlations, we find that the universal conductivity of these models is approximately the same. In particular, the ratio of this value to that of the pure model agrees with recent experiments on nanohole thin film superconductors in a magnetic field, in the large disorder limit.