Since the Superconducting gap vanishes at the critical temperature, the thermal energy gets sufficient to break up almost all the cooper pairs. But, as far as I understood, the supercurrent is solely carried by Cooper pairs, so basically there is no supercurrent just below Tc? This is also justified by the relation that the critical current density is proportional to the gap, so even tiny currents result in a switch into normal phase. So is it then true, that we only have sufficient useful superconductivity far below Tc? And one other question: At any finite temperature it can occur, that a cooper pair gets thermally broken and result in quasiparticles. So turning on an electrical field, they should move and at some point scatter dissipating energy and gaining resistance, which is obviously not the case for superconductors. Whats wrong in my considerations? I could only imagine that somehow the time scale for repairing into Cooper pairs is shorter than the mean scattering time (which statistically would anyway allow dissipative scattering to happen at some point...)
I will be happy for any answer!
