Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields

TL;DR

This paper derives the Ginzburg-Landau functional from the BCS theory under general external fields and provides an asymptotic formula for the critical temperature shift, extending previous results to non-uniform magnetic fields.

Contribution

It extends the microscopic derivation of Ginzburg-Landau theory and critical temperature formulas to general external magnetic and electric fields, including non-uniform magnetic flux.

Findings

Derived Ginzburg-Landau functional from BCS theory with general external fields

Provided an asymptotic formula for the BCS critical temperature shift

Extended previous results to non-uniform magnetic fields with flux

Abstract

We consider the Bardeen-Cooper-Schrieffer (BCS) free energy functional with weak and macroscopic external electric and magnetic fields and derive the Ginzburg-Landau functional. We also provide an asymptotic formula for the BCS critical temperature as a function of the external fields. This extends our previous results in arXiv:2105.05623 for the constant magnetic field to general magnetic fields with a nonzero magnetic flux through the unit cell.