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.