BCS theory

BCS theory is the microscopic explanation of superconductivity, put forward in 1957 by Bardeen, Cooper, and Schrieffer, and it is one of the triumphs of twentieth-century physics: it derived, from the quantum mechanics of electrons and lattice vibrations, why certain metals conduct without resistance. Before it, superconductivity had been a stubborn 46-year-old mystery; after it, the phenomenon was understood from first principles.

The theory rests on the phonon-mediated attraction that binds electrons into Cooper pairs. Its central move is to write the many-electron ground state as a single coherent quantum superposition, the BCS wavefunction, in which the momentum states near the Fermi surface are occupied in correlated pairs rather than one by one. Solving self-consistently yields an energy gap Delta that opens at the Fermi surface, the energy needed to break a pair. The theory makes sharp, testable predictions: the universal ratio 2 Delta(0) is about 3.52 k_B T_c linking the gap to the critical temperature, the isotope effect T_c proportional to M^(-1/2) (heavier ions, lower T_c) that directly confirms phonons are the glue, an exponentially small low-temperature specific heat reflecting the gap, and the Meissner effect. The condensate embodies off-diagonal long-range order, a macroscopic occupation of a single pair state.

BCS theory earned its authors the 1972 Nobel Prize and remains the definitive account of conventional superconductors. Its honest limitation is that it is a weak-coupling theory built specifically on phonon-mediated pairing. It does not explain the high-temperature cuprate superconductors discovered in 1986, nor most other unconventional superconductors, whose pairing mechanism and even symmetry are different and, in several cases, still not fully understood.