Mixed normal-superconducting states in the presence of strong electric currents

TL;DR

This paper analyzes the behavior of superconductors under large electric currents using Ginzburg-Landau equations, revealing mixed normal-superconducting states and the exponential decay of the order parameter in certain regions.

Contribution

It provides new analytical results on the spatial structure of superconducting states under strong currents, including exponential decay estimates in the large  limit.

Findings

Superconductivity is exponentially small in significant parts of the domain under large currents.

Results extend to time-dependent problems and large domain limits.

Identifies conditions for the stability of normal and superconducting states.

Abstract

We study the Ginzburg-Landau equations in the presence of large electric currents, that are smaller than the critical current where the normal state losses its stability. For steady-state solutions in the large $\kappa$ limit, we prove that the superconductivity order parameter is exponentially small in a significant part of the domain, and small in the rest of it. Similar results are obtained for the time-dependent problem, in continuation of the paper by the two first authors [3]. We conclude by obtaining some weaker results, albeit similar, for steady-state solutions in the large domain limit.