BCS theory

In 1953, Brian Pippard, motivated by penetration experiments, proposed that this would modify the London equations via a new scale parameter called the coherence length.

[4] The demonstration that the phase transition is second order, that it reproduces the Meissner effect and the calculations of specific heats and penetration depths appeared in the December 1957 article, "Theory of superconductivity".

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.

Thus, the collective behavior of the condensate is a crucial ingredient necessary for superconductivity.BCS theory starts from the assumption that there is some attraction between electrons, which can overcome the Coulomb repulsion.

In most materials (in low temperature superconductors), this attraction is brought about indirectly by the coupling of electrons to the crystal lattice (as explained above).

For instance, Cooper pairs have been observed in ultracold gases of fermions where a homogeneous magnetic field has been tuned to their Feshbach resonance.

BCS is able to give an approximation for the quantum-mechanical many-body state of the system of (attractively interacting) electrons inside the metal.

The hyperphysics website pages at Georgia State University summarize some key background to BCS theory as follows:[8] BCS derived several important theoretical predictions that are independent of the details of the interaction, since the quantitative predictions mentioned below hold for any sufficiently weak attraction between the electrons and this last condition is fulfilled for many low temperature superconductors - the so-called weak-coupling case.