Stability of supercurrents and condensates in type I superconductors

Excitations of Cooper pairs into non-condensed bound pairs are similar to excitations oftrue bosons out of the Bose-Einstein condensate. Using the Landau criterion ofsuperfluidity we evaluate the critical current above which these pair-excitations wouldlead to a finite resistivity. The predicted value strongly depends on the chosenapproximation. The Thouless approach based on the Galitskii T-matrix and theKadanoff-Martin theory which is in many aspects equivalent to the BCS theory, both lead tozero critical velocity, what is in conflict with the mere existence of supercurrents. Incontrast, the T-matrix with multiple scattering corrections provides the critical velocityof pair excitation which is √3-times larger than the critical velocity of pairbreaking. This agrees with the experimentally well established fact that supercurrents intype I superconductors are limited by pair breaking, not by pair excitation.