Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field

TL;DR

This paper derives the Ginzburg-Landau functional from the BCS theory under a weak magnetic field and provides an asymptotic formula for the critical temperature shift, extending previous results to include magnetic flux effects.

Contribution

It extends the microscopic derivation of Ginzburg-Landau theory and the critical temperature shift to cases with non-zero magnetic flux, building on prior work without flux.

Findings

Derived Ginzburg-Landau functional in magnetic field

Provided asymptotic formula for critical temperature shift

Extended previous results to non-zero magnetic flux

Abstract

Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we derive the Ginzburg-Landau functional in the presence of a weak homogeneous magnetic field. We also provide an asymptotic formula for the BCS critical temperature as a function of the magnetic field. This extends the previous works arXiv:1102.4001 and arXiv:1410.2352 of Frank, Hainzl, Seiringer and Solovej to the case of external magnetic fields with non-vanishing magnetic flux through the unit cell.