The Upper Critical Field in Disordered Two-Dimensional Superconductors

TL;DR

This paper calculates the upper critical field in disordered 2D superconductors, showing no anomalous low-temperature positive curvature with increasing disorder, contrary to previous predictions due to approximation errors.

Contribution

It provides a refined analysis including both perturbative and non-perturbative methods, correcting prior assumptions about the behavior of the critical field in disordered superconductors.

Findings

No anomalous positive curvature observed in critical field.

Previous predictions attributed to unjustified analytical approximations.

Results challenge earlier theoretical expectations.

Abstract

We present calculations of the upper critical field in superconducting films as a function of increasing disorder (as measured by the normal state resistance per square). In contradiction to previous work, we find that there is no anomalous low-temperature positive curvature in the upper critical field as disorder is increased. We show that the previous prediction of this effect is due to an unjustified analytical approximation of sums occuring in the perturbative calculation. Our treatment includes both a careful analysis of first-order perturbation theory, and a non-perturbative resummation technique. No anomalous curvature is found in either case. We present our results in graphical form.