On the first critical field in the 3D Ginzburg-Landau model of superconductivity

TL;DR

This paper estimates the first critical magnetic field in the 3D Ginzburg-Landau model for superconductivity with large parameters, characterizing vortexless solutions below and near this threshold.

Contribution

It provides a precise estimate of the first critical field and analyzes the behavior of Meissner solutions in the large Ginzburg-Landau parameter regime.

Findings

Estimated the first critical field for large Ginzburg-Landau parameter.

Characterized the Meissner solution below the critical field.

Demonstrated existence of a local energy minimizer near the critical field.

Abstract

The Ginzburg-Landau model is a phenomenological description of superconductivity. A crucial feature of type-II superconductors is the occurrence of vortices, which appear above a certain value of the applied magnetic field called the first critical field. In this paper we estimate this value, when the Ginzburg-Landau parameter is large, and we characterize the behavior of the Meissner solution, the unique vortexless configuration that globally minimizes the Ginzburg-Landau energy below the first critical field. In addition, we show that beyond this value, for a certain range of the strength of the applied field, there exists a unique Meissner-type solution that locally minimizes the energy.