BCS theory - More details

A quantum theory of superconductivity; developed by John Bardeen, Leon Cooper, and John Schrieffer in 1957. Bound states of two electrons (Cooper pairs) form, which account for zero electrical resistance and the Meissner effect. There has been experimental verification of the prediction that magnetic fields through a superconducting ring should have values that are multiples of a basic magnetic unit (the fluxoid).

BCS theory (named for its creators, Bardeen, Cooper, and Schrieffer) explains conventional superconductivity, the ability of certain metals at low temperatures to conduct electricity without electrical resistance.

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). If this binding energy is higher than the energy provided by kicks from oscillating atoms in the conductor (which is true at low temperatures), then the electron pair will stick together and resist all kicks, thus not experiencing resistance.

More details

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). The original results of BCS (discussed below) described an "s-wave" superconducting state, which is the rule among low-temperature superconductors but is not realized in many "unconventional superconductors", such as the "d-wave" high-temperature superconductors.

BCS were able to give an approximation for the quantum-mechanical state of the system of (attractively interacting) electrons inside the metal. Whereas in the normal metal electrons move independently, in the BCS state they are bound into "Cooper pairs" by the attractive interaction.

BCS have derived several important theoretical predictions that are independent of the details of the interaction (the quantitative predictions mentioned below hold only for sufficiently weak attraction between the electrons, which is however fulfilled for many low temperature superconductors - the so-called "weak-coupling case"). These have been confirmed in numerous experiments:

Since the electrons are bound into Cooper pairs, a finite amount of energy is needed to break these apart into two independent electrons. This means there is an "energy gap" for "single-particle excitation", unlike in the normal metal (where the state of an electron can be changed by adding an arbitrarily small amount of energy). This energy gap is highest at low temperatures but vanishes at the transition temperature when superconductivity ceases to exist. BCS theory correctly predicts the variation of this gap with temperature. The ratio between the value of the energy gap at zero temperature and the value of the superconducting transition temperature (expressed in energy units) takes the universal value of 3.5, independent of material. Due to the energy gap, the specific heat of the superconductor is suppressed strongly (exponentially) at low temperatures, there being no thermal excitations left. However, before reaching the transition temperature, the specific heat of the superconductor becomes even higher than that of the normal conductor (measured immediately above the transition) and the ratio of these two values is found to be universally given by 2.5. the expulsion of a magnetic field from the superconductor and the variation of the penetration depth (the extent of the screening currents flowing below the metal's surface) with temperature. It also describes the variation of the critical magnetic field (above which the superconductor can no longer expel the field but becomes normalconducting) with temperature. BCS theory relates the value of the critical field at zero temperature to the value of the transition temperature and the density of states at the Fermi energy.