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BCS theory Created 2026-09-24 Updated 2026-10-18
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.