# 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.

### Cooper Pair Formation

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:

 Left: Cooper pair formation - electron-phonon interaction: the electron is attracted to the positive charge density (red glow) created by the first electron distorting the lattice around itself.

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.

### Cooper Pairs - BCS Theory Supercurrent Carriers

The Cooper pairs within the superconductor are what carry the supercurrent, but why do they experience such perfect conductivity?
Mathematically, because the Cooper pair is more stable than a single electron within the lattice, it experiences less resistance (although the superconducting state cannot be made up entirely of Cooper pairs as this would lead to the collapse of the state).
Physically, the Cooper pair is more resistant to vibrations within the lattice as the attraction to its partner will keep it 'on course' - therefore, Cooper pairs move through the lattice relatively unaffected by thermal vibrations (electron-phonon interactions) below the critical temperature. Play the animations below by clicking the 'play' icon in the corner to compare Cooper pair superconduction and normal conduction.

 Above: Cooper pairs carry the supercurrent relatively unresisted by thermal vibrations. Above: Conventional conduction is resisted by thermal vibrations within the lattice.

### 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 pairs.
1986 saw the discovery of high temperature superconductors (see History) which broke this limit (the highest known today is in excess of 150K) - it is in debate as to what mechanism prevails at higher temperatures, as BCS cannot account for this. See High Temperature Superconductivity Theory next for further details.