Microscopic Theory of Superconductivity

Abstract:

SINCE the discovery of the isotope effect, it has been known that superconductivity arises from the interaction between electrons and lattice vibrations, but it has proved difficult to construct an adequate theory based on this concept. As has been shown by Fröhlich,¹ and in a more complete analysis by Bardeen and Pines² in which Coulomb effects were included, interactions between electrons and the phonon field lead to an interaction between electrons which may be expressed in the form

where |M_κ|² is the matrix element for the electronphonon interaction for the phonon wave vector κ, calculated for the zero-point amplitude of the vibrations, the c's are creation and destruction operators for the electrons in the Bloch states specified by the wave vector k and spin s, and H_Coul represents the screened Coulomb interaction…