Dissemination of IT for the Promotion of Materials Science (DoITPoMS)


BCS theory

We are now almost in a position to be able to explain how type I superconductivity arises, but first we need to look at some quantum properties and how electrons are arranged in normal solids and how this differs when the transition is made to the superconducting state.

We know that in normal electronic conduction the electrons that carry the current are scattered by impurities and lattice vibrations that interrupt their motion. In superconductors, however, the superconducting current is carried by Cooper pairs that have to be scattered as a single object without being broken apart. For the electrons which make up the pair to be scattered and produce an interaction we observe as electrical resistance, the Cooper pair must be split apart. This act requires an energy at least equal to the energy gap produced by the binding energy of the Cooper pairs.

Due to random energy fluctuations, even at temperatures below Tc, there will sometimes be enough energy to break the pair and alter the momentum of the electrons. In order to stop the current, however, all of the pairs must be broken which would require a considerable combined effort. As the total energy of the system increases as the temperature is raised and approaches Tc, more and more pairs are broken as electrons are excited above the energy gap. At the transition temperature there are no Cooper pairs left.

Theoreticians often consider the breaking of Cooper pairs as a creation of excitations which consist of electrons which were previously regarded as a bound pair. These “free electrons” are referred to as quasi-particles. At any temperature above 0 K there will be both bound pairs and quasi-particles present. This has striking similarities to the two fluid model which was proposed as a purely phenomenological model.