Existence and stability of superconducting solutions for the Ginzburg-Landau equations in the presence of weak electric currents

TL;DR

This paper proves the existence and linear stability of superconducting solutions in a simplified Ginzburg-Landau model under weak electric currents, highlighting conditions near the purely superconducting state.

Contribution

It establishes the existence and stability of superconducting solutions in a reduced Ginzburg-Landau model with weak electric currents, a novel analytical result.

Findings

Existence of steady-state superconducting solutions near the pure state.

Linear stability of these solutions under weak electric currents.

Validation of the model's predictions for superconducting stability.

Abstract

For a reduced Ginzburg-Landau model in which the magnetic field is neglected, we prove, for weak electric currents, the existence of a steady-state solution in a vicinity of the purely superconducting state. We further show that this solution is linearly stable.