General pairing theory for condensed and non-condensed pairs of a superconductor in a high magnetic field

Abstract

We extend Gor'kov theory to address superconducting pairing at high magnetic fields and general temperatures with arbitrary attractive interaction strength. This analysis begins with a new interpretation of the high-field Gor'kov gap equation which we associate with an instability in a generalized particle-particle ladder series. Importantly, this interpretation of the non-linear gap equation enables a treatment of pairing which is distinct from condensation. We also show how to consolidate two distinct fermionic pairing schemes in real and momentum space, both corresponding to an Abrikosov lattice. Numerical results for the fermionic local density of states demonstrate that gapless structure in a field is robust and presumably relevant to quantum oscillation experiments. We find that despite their differences, both pairing schemes contain very similar physics. Our formalism is designed to explore a variety of magnetic field effects in the so-called pseudogap phase and throughout the BCS-BEC crossover.