The ground state energy of the three dimensional Ginzburg-Landau functional. Part~II: Surface regime

TL;DR

This paper rigorously analyzes the Ginzburg-Landau model in three dimensions under strong magnetic fields, confirming that superconductivity is confined near the boundary above the second critical field and detailing the transition from bulk to surface superconductivity.

Contribution

It provides rigorous mathematical proof that superconductivity localizes near the boundary in the surface regime and offers precise energy estimates around the second critical field.

Findings

Superconductivity is confined near the boundary above the second critical field.

Energy estimates accurately describe the transition from bulk to surface superconductivity.

The results confirm physical predictions about the surface regime in 3D Ginzburg-Landau models.

Abstract

We study the Ginzburg-Landau model of superconductivity in three dimensions and for strong external magnetic fields. For magnetic field strengths above the phenomenologically defined second critical field it is known from Physics that superconductivity should be essentially restricted to a region near the boundary. We prove that the expected region does indeed carry superconductivity. Furthermore, we give precise energy estimates valid also in the regime around the second critical field which display the transition from bulk superconductivity to surface superconductivity.