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

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.

32 pages

References in corpus (2)

• Vortex density models for superconductivity and superfluidity
• 3D vortex approximation construction and $\epsilon$-level estimates for the Ginzburg-Landau functional

Cited by in corpus (3)

• Bounded vorticity for the 3D Ginzburg-Landau model and an isoflux problem
• On the Meissner state for type-II inhomogeneous superconductors
• Wrinkling of an elastic sheet floating on a liquid sphere