Hi, I am fairly new to superconductivity (introductory college level). I have covered and grasped the basics but was wondering if someone could shed some light on what specifically causes materials to have zero resistance when they become superconducting. I know that cooper pairs form when the material is in a low energy state (10-100 kelvin). These cooper pairs have integer spins meaning they form composite bosons. The lattice vibrational energy (phonons) are also bosons. But what is it about these quantum mechanical effects that specifically causes zero resistance to arise? Does it have something to do with Pauli's Exclusion Principle as i have seen that some websites mention this but do not explain its significance in superconductivity?
The gap is not crucial for zero resistivity as there are also zero gap superconductors. The point is that the Cooper pairs form a Bose-Einstein condensate. In a current carrying superconductor, all cooper pairs move with the same velocity. This state is metastable as breaking ( and decelerating ) only some Cooper pairs corresponds to excited states. Only if there are sufficiently many excited states carrying zero momentum so that these can form an alternative Bose-Einstein condensate of lower energy, superconductivity will break down. The probability for such a number of pairs being excited by scattering at the same time by chance is arbitrary low. If there are too few excited states to form a Bose-Einstein condensate on their own they have no other possibility to recombine into the original current carrying condensate.
What are zero gap superconductors? Could you give some examples? Do you mean zero gap in some directions but not in others as d-wave cuprates?
I think the following article is quite illuminating: Brun Hansen, Infinite conductivity of ordinary and gapless superconductors. Physica Vol. 39, pp. 271-292, Year 1968