What is the correct explanation of why superconductivity occurs in metals when they are cooled to a temperature below $T_c$?
My textbook has the following explanation:
Superconductivity is the phenomenon exhibited by certain metals (type 1 superconductors only) where they will have no resistance to the flow of electricity when their temperature is cooled below the critical temperature. In superconductors above the critical temperature (Tc) of normal conductors, the thermal vibrations of the lattice structure lead to collisions between electrons and the lattice, which impede electron movement and contribute to the resistance of these materials. BCS theory (Bardeen, Cooper and Schrieffer) describes the occurrence of electron pairs and phonons in superconductors below their critical temperature, allowing the movement of electrons without collisions or resistance. Below the critical temperature, lattice vibrations in a superconductor become negligible, so the predominant interaction between electrons and the lattice structure is electrostatic attraction. An electron moving through the lattice will attract positive ions towards itself to create a ‘trough’ of concentrated positive charge density, which attracts a 2nd trailing electron, creating a Cooper pair with the 1st electron. The distortion of the crystal lattice by the leading electron creates/emits a packet of vibrational energy (a phonon) which is absorbed by the trailing electron (phonons hold electrons together). This transfer of energy allows the electrostatic repulsion existing between negative electrons to be overcome in the formation of Cooper pairs. Cooper pairs are continually formed, broken and reformed between different electrons, allowing them to move through the lattice coherently, without collision and thus, without resistance.
But this is the simplified explanation, right? Could you please give me the proper explanation or just give me a link where I can read a good explanation? I did a Google search and most of the explanations aren't satisfactory. My teacher said a proper explanation would have to involve Bose Einstein condensates and quantum physics but I can't find any explanations on the internet that mention this.
