I'm a little out of my depth here...
I'm trying to understand quasiparticle tunnelling in superconductor-insulator-superconductor junctions. Many books use the "semiconductor model" to explain this:
These diagrams show the available quasiparticle states (with a large band gap due to the formation of Cooper pairs), the filled states, and the empty states.
My question with these diagrams is: shouldn't all the electrons exist as Cooper pairs? I assume that the lower band is filled with quasiparticles, since Cooper pairs would all be at the same energy level and quasiparticles obey Fermi-Dirac statistics, but I don't know where they're coming from.
Also, why is there an energy gap in the quasiparticle energy states? I understand that this gap corresponds to the energy needed to break Cooper pairs, but I don't understand why would you need to break Cooper pairs to raise the energy of quasiparticles.
Or is this "semiconductor model" not fully representative of the physics?