VALIDITY OF THE GORKOV EXPANSION NEAR THE UPPER CRITICAL-FIELD IN TYPE-II SUPERCONDUCTORS

We have examined the validity of the Gor'kov expansion in the strength of the order parameter of type II superconductors near the upper crit ical field. Although the degeneracy of the electron levels in a magnet ic field gives non-perturbative terms in the solution to the Bogoliubo v-de Gennes equations we find, contrary to recent claims, that these n on-perturbative terms cancel in the expression for the thermodynamic p otential, and that the traditional Gor'kov theory is correct sufficien tly close to H-c2 at finite temperature. We have derived conditions fo r the validity of the Gor'kov theory which essentially state that the change in the quasiparticle energies as compared to the normal-state e nergies cannot be too large compared to the temperature.