Microscopic derivation of Ginzburg-Landau theory and the BCS critical temperature shift in general external fields.

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 Deuchert et al. (Microscopic derivation of Ginzburg-Landau theory and the BCS critical temperature shift in a weak homogeneous magnetic field, PMP (1), 1-89 (2023)) for the constant magnetic field to general magnetic fields with a nonzero magnetic flux through the unit cell.