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A Cooper pair is the name given to electrons that are bound together in a certain manner first described by Leon Cooper. Cooper showed that an arbitrarily small attraction between electrons in a metal can cause a paired state of electrons to have a lower energy than the Fermi energy, which implies that the pair is bound. In normal superconductors, this attraction is due to the electron phonon interaction. The Cooper Pair state forms the basis of the BCS theory of superconductivity developed by John Bardeen, John Schrieffer and Leon Cooper for which they shared the 1972 Nobel Prize. Image File history File links Broom_icon. ... Leon N Cooper (born February 28, 1930) is an American physicist and winner of the 1972 Nobel Prize for Physics, along with John Bardeen and John Robert Schrieffer, for his role in developing the BCS theory (named for their initials) of superconductivity, work he did in his 20s. ... The Fermi energy is a concept in quantum mechanics referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature. ... For other uses, see Electron (disambiguation). ... Normal modes of vibration progression through a crystal. ... BCS theory (named for its creators, Bardeen, Cooper, and Schrieffer) successfully explains conventional superconductivity, the ability of certain metals at low temperatures to conduct electricity without resistance. ... John Bardeen (May 23, 1908 – January 30, 1991) was an American physicist and electrical engineer. ... John Robert Schrieffer (born May 31, 1931) is an American physicist and winner, with John Bardeen and Leon Neil Cooper, of the 1972 Nobel Prize for Physics for developing the BCS theory (for their initials), the first successful microscopic theory of superconductivity. ... Leon N Cooper (born February 28, 1930) is an American physicist and winner of the 1972 Nobel Prize for Physics, along with John Bardeen and John Robert Schrieffer, for his role in developing the BCS theory (named for their initials) of superconductivity, work he did in his 20s. ... The Nobel Prize (Swedish: ) was established in Alfred Nobels will in 1895, and it was first awarded in Physics, Chemistry, Physiology or Medicine, Literature, and Peace in 1901. ...

A simplified explanation: an electron in a metal normally behaves as basically a free particle. The electron is repelled from other electrons due to their similar charge, but it also attracts the positive ions that make up the rigid lattice of the metal. This attraction can distort the positively charged ions in such a way as to attract other electrons (the electron-phonon interaction). This attraction due to the displaced ions can overcome the electrons repulsion due to the electrons having the same charge and cause them to pair-up. Generally, the pairing only occurs at low temperatures and is quite weak, meaning the paired electrons may still be many hundreds of nanometers apart. Look up charge in Wiktionary, the free dictionary. ... A nanometre (American spelling: nanometer, symbol nm) (Greek: νάνος, nanos, dwarf; μετρώ, metrό, count) is a unit of length in the metric system, equal to one billionth of a metre (or one millionth of a millimetre), which is the current SI base unit of length. ...

Cooper originally just considered the case of an isolated pair forming in a metal. When one considers the more realistic state consisting of many electrons forming pairs as is done in the full BCS Theory one finds that the pairing 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, since small excitations such as scattering of electrons are forbidden.

Herbert Fröhlich was first to suggest that the electrons might act as pairs coupled by lattice vibrations in the material. This was indicated by the isotope effect observed in superconductors. The isotope effect showed that materials with heavier ions (different nuclear isotopes) had lower superconducting transition temperatures. This can be explained nicely by the theory of Cooper pairing; since heavier ions are harder to move they would be less able to attract the electrons resulting in a smaller binding energy for Cooper pairs. Herbert Fröhlich was a British scientist and a Fellow of the Royal Society. ... hey!! I hate you!! isotopes are the elements that have different no. ... For other uses, see Isotope (disambiguation). ...

The pair are still Cooperic if k₁ = k₂ and k₁ − q = − (k₁ − q) = − ( − k₂ − q) = − (k₂ + q)

The theory of Cooper pairs is quite general and does not depend on the specific electron-phonon interaction. Condensed matter theorists have proposed pairing mechanisms based on other attractive interactions such as electron-exciton interactions or electron-plasmon interactions. Currently, none of these alternate pairing interactions has been observed in any material. This page is about the quasiparticle. ... In physics, the plasmon is the quasiparticle resulting from the quantization of plasma oscillations just as photons and phonons are quantizations of light and sound waves, respectively. ...

References

Original reference: L. N. Cooper, "Bound Electron Pairs in a Degenerate Fermi Gas", Phys. Rev. 104 (4), 1189 (1956).

See also

• BCS theory
• Superconductivity