BCS theory - proposed by Bardeen, Cooper, and Schrieffer in 1957 - is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state.
The mid-1950s saw rapid progress in the understanding of superconductivity. It began in the 1948 paper, On the Problem of the Molecular Theory of Superconductivity where Fritz London proposed that the phenomenological London equations may be consequences of the coherence of a quantum state. In 1953, Brian Pippard, motivated by penetration experiments, proposed that this would modify the London equations via a new scale parameter called the coherence length. John Bardeen then argued in the 1955 paper, Theory of the Meissner Effect in Superconductors that such a modification naturally occurs in a theory with an energy gap. The key ingredient was Leon Neil Cooper's calculation of the bound states of electrons subject to an attractive force in his 1956 paper, Bound Electron Pairs in a Degenerate Fermi Gas.
In 1957 Bardeen and Cooper assembled these ingredients and constructed such a theory, the BCS theory, with Robert Schrieffer. The theory was first announced in February 1957 in the letter, Microscopic theory of superconductivity. The demonstration that the phase transition is second order, that it reproduces the Meissner effect and the calculations of specific heats and penetration depths appeared in the July 1957 article, Theory of superconductivity. They received the Nobel Prize in Physics in 1972 for this theory. The 1950 Landau-Ginzburg theory of superconductivity is not cited in either of the BCS papers.
In 1986, "high-temperature superconductivity" was discovered (i.e. superconductivity at temperatures considerably above the previous limit of about 30 K; up to about 130 K). It is believed that at these temperatures other effects are at play; these effects are not yet fully understood. (It is possible that these unknown effects also control superconductivity even at low temperatures for some materials).
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