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

TL;DR

This paper investigates the applicability of Gor'kov's expansion near the upper critical field in type II superconductors, confirming its validity under certain conditions despite potential non-perturbative effects.

Contribution

The study demonstrates that non-perturbative terms cancel out in the thermodynamic potential, validating Gor'kov theory near Hc2 at finite temperature, and derives conditions for its validity.

Findings

Non-perturbative terms cancel in thermodynamic potential.

Gor'kov theory remains valid close to Hc2 at finite temperature.

Validity depends on quasiparticle energy changes relative to temperature.

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 Hc2 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.