BCS Superconductivity Theory
In 1957, Bardeen, Cooper and Schrieffer (BCS) proposed a theory that explained the microscopic origins of superconductivity, and could quantitatively predict the properties of superconductors. Prior to this, there was Ginzburg-Landau theory, suggested in 1950, which was a macroscopic theory. This will not be dealt with here, but Ginzburg-Landau theory can be derived from BCS theory.
Mathematically, BCS theory is complex, but relies on an earlier 'discovery' by Cooper (1956), who showed that the ground state of a material is unstable with respect to pairs of 'bound' electrons. These pairs are known as Cooper pairs and are formed by electron-phonon interactions - an electron in the cation lattice will distort the lattice around it, creating an area of greater positive charge density around itself. Another electron at some distance in the lattice is then attracted to this charge distortion (phonon) - the electron-phonon interaction. The electrons are thus indirectly attracted to each other and form a Cooper pair - an attraction between two electrons mediated by the lattice which creates a 'bound' state of the two electrons:
The formation of Cooper pairs is supported by the fact that BCS and the Ginzburg-Landau theories predict the charge and mass of the supercurrent 'particle' to be 2e and 2Me respectively.
The Cooper pairs within the superconductor are what carry the supercurrent,
but why do they experience such perfect conductivity?
High Temperature Superconduction
However, BCS theory predicted a theoretical maximum to Tc
of around 30-40K, as above this, thermal energy would cause electron-phonon
interactions of an energy too high to allow formation of or sustain Cooper