Why is there an energy gap in superconductors?

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:

(source: wikimedia.org)

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?

• Simple matter with superconductivity : in a bulk system, there is no electrons, there are Cooper pairs which correspond to an other vacuum than the Fermi sea. In both bulk and heterostructures, excitations of the superconducting ground state are called (Bogoliubov) quasi-particles (BQP). The band-gap is a forbidden region of energy for the BQP in a bulk. Heterostructure are a bit more cumbersome, with different energy scales depending on the microscopic details (called proximity effect usually). We only discuss BQP in heterostructures, and the diagram refer to them. Aug 5, 2015 at 9:02

The lower part is not filled with quasi-particles. At zero Kelvin, in zero magnetic field and with zero disorder all free electrons condense and form the superconducting condensate. The semiconductor model now describes the breaking of Cooper pairs not as resulting in two electron-, but in one electron- and hole-like excitation. As you are potentially familiar with in semiconductors, one electron of energy $E$ above the Fermi level may be described by one hole with the same energy below.