BCS theory describes a superconducting instability caused by attractive interactions between opposite-momentum fermions near a Fermi surface.
The Cooper instability is the logarithmic growth of an attractive BCS coupling at low energy. If is the density of states and , perturbation theory breaks down at a scale proportional to .
At zero temperature and weak coupling, the BCS gap equation gives . Its exponential scale agrees with the renormalization-group scale of the Cooper instability.
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Main theory to explain Type I superconductors very successfully.
TODO can someone please just give the final predictions of BCS, and how they compare to experiments, first of all? Then derive them.
High level concepts:
- the wave functions of pairs of electrons (fermions) get together to form bosons. This is a phase transition effect, thus the specific sudden transition temperature.
- the pairs form a Bose-Einstein condensate
- once this new state is reached, all pairs are somehow entangled into one big wave function, and you so individual lattice imperfections can't move just one single electron off trajectory and make it lose energy