BCS theory

At sufficiently low temperatures, electrons near the Fermi surface become unstable against the formation of Cooper pairs. Cooper showed such binding will occur in the presence of an attractive potential, no matter how weak. In conventional superconductors, an attraction is generally attributed to an electron-lattice interaction. The BCS theory, however, requires only that the potential be attractive, regardless of its origin. In the BCS framework, superconductivity is a macroscopic effect which results from “condensation” of Cooper pairs. These have some bosonic properties, while bosons, at sufficiently low temperature, can form a large Bose-Einstein condensate. Superconductivity was simultaneously explained by Nikolay Bogoliubov, by means of the so-called Bogoliubov transformations.

In many superconductors, the attractive interaction between electrons (necessary for pairing) is brought about indirectly by the interaction between the electrons and the vibrating crystal lattice (the phonons). Roughly speaking the picture is the following:

An electron moving through a conductor will attract nearby positive charges in the lattice. This deformation of the lattice causes another electron, with opposite “spin”, to move into the region of higher positive charge density. The two electrons then become correlated. There are a lot of such electron pairs in a superconductor, so that they overlap very strongly, forming a highly collective “condensate”. Breaking of one pair results in changing of energies of remained macroscopic number of pairs. If the required energy is higher than the energy provided by kicks from oscillating atoms in the conductor (which is true at low temperatures), then the electrons will stay paired and resist all kicks, thus not experiencing resistance. Thus, the collective behaviour of “condensate” is a crucial ingredient of superconductors.

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