Cooper pair
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Cooper pairs result from interactions between conduction band electrons and the ion lattice in which they move, such as the Pierels effect or Jahn-Teller distortion. Electrons in vacuum and most solids repel each other due to their like charges, but in highly polarizable materials, such as metals, interactions between the polarized lattice and electrons may overcome the repulsion and result in bound electron pairs, Cooper pairs. A simplified explanation: a free electron in a metal weakly attracts the positively charged ions around it. If the attraction is strong enough, other electrons can be attracted to this built-up positive charge and hence follows the other electron around, resulting in pairing. Generally, the pairing is quite weak, meaning the paired electrons may be many hundreds of nanometers apart.
Electrons are fermions, and as such have a relatively high kinetic energy even at zero temperature, due to the Pauli exclusion principle, which restricts the number of electrons which may have low energy. However, Cooper pairs are bosons, which have no such restrictions. Thus as long as there are no pair-breaking effects, such as temperature or magnetic fields, the paired state has lower energy. At sufficiently low temperature and high pair density, the pairs may form a Bose-Einstein condensate.
Pair condensation is the basis for the BCS theory of superconductivity. The effective net attraction between the normally repulsive electrons produces a pair binding energy on the order of milli-electron volts, enough to keep them paired at extremely low temperatures, normally about 2-4 Kelvin.
The transition of a metal from normal to superconducting is a condensation, rather like the superfluid transition of Helium. This transition opens a gap in the continuous spectrum of allowed energy states of the electrons, meaning that all excitations of the system must possess some minimum amount of energy. This gap to excitations leads to superconductivity and superfluidity, since small excitations such as scattering of electrons or viscosity of liquid Helium are forbidden.
Froehlich was first to suggest that the electrons act as pairs coupled by lattice vibrations in the material. This coupling is viewed as an exchange of phonons, phonons being the quanta of lattice vibration. Since phonons reflect the structure of the lattice, and heavier ions vibrate more slowly, different nuclear isotopes of a superconducting element should show different behavior. This is indeed observed, and it is called the isotope effect. The boson-like behavior of such electron pairs was further investigated by Leon Cooper and hence they are called "Cooper pairs".
