ABSTRACT
In this chapter, the authors explore the successful microscopic theory of superconductivity, which was published in 1957 by J. Bardeen, John Cooper and J. R. Schrieffer—the BCS theory. They provide a discussion on the compact formalism of second quantization. The current-carrying state for a superconductor proposed by BCS has some of the properties of a system of bound pairs of electrons. BCS theory has been very successful in describing conventional low-temperature superconductivity. Bardeen, Cooper and Schrieffer assumed that mutual attraction was due to polarization of the ionic lattice by the electrons, but in considering more exotic types of superconductivity it is important to remember that according to their theory any mechanism leading to an attractive interaction near the Fermi surface can lead to superconductivity. The best and most direct evidence for the importance in superconductivity of the electron-phonon-electron interaction comes not from the isotope effect but from the tunnelling density of states.
