On the thermodynamics of weak-coupling superconductors

Abstract

The effect of the electron-phonon renormalisation on the thermodynamics of weak coupling superconductors is discussed, starting from the equations appropriate for a strong-coupling system derived by Bardeen and Stephen (1964). For isotropic superconductors, the expected factor of (1+ lambda ), where lambda is the mass renormalisation parameter, is obtained. It cancels out of the various ratios of experimental quantities, giving just the BCS results. In order to re-derive the usual results for the anisotropic superconductor, with the effect of the mass renormalisation explicitly included, it is necessary to modify the definition of the Fermi surface average to include the quasiparticle velocity. Some of the difficulties of trying to obtain similar results, starting from the formulae derived by Wadal (1964), are also discussed. A simple way to include corrections due to deviations of 2 delta 0/kBTc from its BCS value, is given.