Validity of the Gor'kov expansion near the upper critical field in type II superconductors

Abstract

We have examined the validity of the Gor'kov expansion in the strength of the order parameter of type II superconductors near the upper critical field. Although the degeneracy of the electron levels in a magnetic field gives non-perturbative terms in the solution to the Bogoliubov - de Gennes equations we find, contrary to recent claims, that these non-perturbative terms cancel in the expression for the thermodynamic potential, and that the traditional Gor'kov theory is correct sufficiently close to at finite temperature. We have derived conditions for the validity of the Gor'kov theory which essentially state that the change in the quasiparticle energies as compared to the normal-state energies cannot be too large compared to the temperature.