= BCS theory
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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>.<Theory of Superconductivity by John Bardeen and others>[pp.1175–1177, introduction and microscopic pairing mechanism]{ref}
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.<Theory of Superconductivity by John Bardeen and others>[p.1177, footnote 18 and coherence-distance discussion]{ref}
Two complementary clues made the microscopic problem concrete. The <superconducting isotope effect> connected the transition to <phonons>.<Electron-Phonon Interactions and Superconductivity by John Bardeen>[p.55, isotope effect as a clue to the microscopic mechanism]{ref}
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.<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]{ref}
The later <Giaever superconducting tunnelling experiment> provided another way to resolve the <superconducting energy gap> through <quantum tunnelling>.<Electron-Phonon Interactions and Superconductivity by John Bardeen>[p.61, section 4, tunnelling conductance and the superconducting density of states]{ref} 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.
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