BardeenCooperSchrieffer

Bardeen-Cooper-Schrieffer theory, commonly known as BCS theory, is a microscopic explanation of conventional superconductivity. Proposed in 1957 by John Bardeen, Leon Cooper, and Robert Schrieffer, it describes how electrons in a metal can form bound pairs, called Cooper pairs, due to an effective attractive interaction mediated by lattice vibrations (phonons). These pairs condense into a macroscopic quantum state that can carry electric current without resistance.

In a metal, electrons near the Fermi surface attract each other via phonon exchange, forming pairs with opposite momenta and spins. The many-body ground state is a coherent superposition of paired states, described by the BCS wavefunction. The pairing opens an energy gap, Delta, at the Fermi surface, which protects the superconducting state against small thermal excitations.

Consequences and predictions of the theory include the Meissner effect, zero direct-current resistance, and characteristic thermodynamic behavior such as an exponential suppression of the electronic specific heat at low temperatures, and a jump in heat capacity at the critical temperature Tc. It also accounts for the isotope effect, with Tc varying roughly inversely with the square root of the atomic mass. The formalism uses Bogoliubov transformations and introduces quasiparticles, sometimes described as bogoliubov quasiparticles, that encode the excitations of the superconducting state.

Scope and limitations: BCS successfully describes many conventional, weak-coupling superconductors and provides a foundational framework for understanding superconductivity. It is less adequate for high-temperature superconductors, where strong coupling and other mechanisms are important; extensions such as Eliashberg theory address more detailed electron-phonon interactions.