This is what I learned from textbook. An insulator is insulate as the gap between the valence band and the conduction band and the fermi level lies in the gap. A superconductor is super electronically conductive because there is a gap between the BCS ground state with the first excited state. This gap prevents electrons from being backscattered. I'm trying to understand why both have gaps but one is insulator, the other is superconductor.
[Physics] the difference of the gap between superconductor and insulator
insulatorssuperconductivity
Best Answer
The difference is that in a normal conductor the current is carried by fermions (i.e. electrons) while in a superconductor the current is carried by bosons (i.e. Cooper pairs).
Have a read through my answer to What is it about the "conduction band" of a material that is distinct from the valence band? where I explain why a full energy band cannot carry a current. In a conventional conductor any momentum eigenstate in the band can be occupied by at most two electrons (with opposite spins) so in a full band the net momentum of the electrons in the band is zero i.e. there is no net drift velocity and hence no current.
In a superconductor the electrons pair up into Cooper pairs that obey Bose-Einstein statistics, so any number of Cooper pairs can occupy the same momentum state. That means the electrons joined into Cooper pairs can have a net momentum, and hence a net drift velocity, so they can carry a current.