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
Articles by others on the same topic
BCS theory describes a superconducting instability caused by attractive interactions between opposite-momentum fermions near a Fermi surface.
John Bardeen, Leon Neil Cooper and John Robert Schrieffer developed BCS theory in 1957, using attraction mediated by phonons.[ref]
Theory of Superconductivity by John Bardeen and others. pp.1175–1177, introduction and microscopic pairing mechanism
Weak-coupling Cooper pairs overlap. The Cooper instability reorganizes an unpaired Fermi surface; it is not Bose-Einstein condensation of compact, pre-existing molecules. The original paper explicitly distinguishes these pictures.[ref]
Theory of Superconductivity by John Bardeen and others. p.1177, footnote 18 and coherence-distance discussion
Two complementary clues made the microscopic problem concrete. The superconducting isotope effect connected the transition to phonons.[ref]
Electron-Phonon Interactions and Superconductivity by John Bardeen. p.55, isotope effect as a clue to the microscopic mechanism
A 1957 transmission experiment used thin lead and tin films as samples in far-infrared and millimeter-microwave measurements. The measured transmission was converted to complex electrical conductivity, normalized to the normal-state value. Comparing film thickness, resistance, annealing and the two metals tested the response's reproducibility. Weak low-photon-energy absorption followed by an onset supported a superconducting energy gap; its extraction required a thin-film electrodynamic model.[ref]
Conductivity of Superconducting Films for Photon Energies between 0.3 and 40kTc by R. E. Glover III and M. Tinkham. Abstract: sample metals, transmission method, normal-state normalization and comparisons; inferred excitation gap
The later Giaever superconducting tunnelling experiment provided another way to resolve the superconducting energy gap through quantum tunnelling.[ref]
Electron-Phonon Interactions and Superconductivity by John Bardeen. p.61, section 4, tunnelling conductance and the superconducting density of states
The derivations below explain what the model predicts, including the distinction between a single quasiparticle's minimum energy and the threshold for making two of them.