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

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