I can't get a definitive explanation of why superconductivity happens and I am getting mixed explanations from my textbooks. I will tell you what I know and hopefully you can correct any misunderstandings I have:
A metal consists of an ionic lattice because the electrons in the valence band have 'jumped' to the conduction band
When a potential difference is applied across a conductor, electrons would move towards the positive potential but the lattice will become distorted as the ions are attracted to the electrons
This creates a region that has dense positive charge. Electrons would be attracted towards this region. However, electrons repel each other and don't want to be close to each other, additionally, Wolfgang Pauli's exclusion principle states that no two fermions can occupy the same quantum state so every two electrons have to combine and form a Bose Einstein condensate as bosons can occupy the same quantum state.
Cooper pairs arise because of the exchange of phonons. Phonons are a collection of excitations of atoms or molecules. The atoms or molecules have to be vibrating in some collective mode.
The bond between two electrons in a boson is very weak, 10^-3 eV. Therefore, the temperature of the metal must be 10 Kelvin for the cooper pairs to exist (using E=kT where k is 10^-4 eV).
Bosons do not interact with matter, hence, they aren't impeded by the lattice.
There are three things I do not understand about this explanation:
Why bosons can be in the same energy state and fermions can't.