Stability of super-currents and condensates in type I superconductors

Excitations of Cooper pairs into non-condensed bound pairs are similar to excitations of true bosons out of the Bose-Einstein condensate. Using the Landau criterion of superfluidity we evaluate the critical current above which these pair-excitations would lead to a finite resistivity. The predicted value strongly depends on the chosen approximation. The Kadanoff-Martin theory which is in many aspects equivalent to the BCS theory, leads to zero critical velocity, what is in conflict with the mere existence of super-currents. In contrast, the T-matrix with multiple scattering corrections provides the critical velocity of pair excitation which is √(3)-times larger than the critical velocity of pair breaking. This agrees with the experimentally well established fact that super-currents in type I superconductors are limited by pair breaking, not by pair excitation.