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Cooper pair
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Cooper pair
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{{Short description|Pair of electrons bound together at low temperature, allowing for superconductivity}}In condensed matter physics, a Cooper pair or BCS pair (BardeenâCooperâSchrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper.“MEMBERWIDE">- the content below is remote from Wikipedia
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Description
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 conventional superconductors, this attraction is due to the electronâphonon interaction. The Cooper pair state is responsible for superconductivity, as described in the BCS theory developed by John Bardeen, Leon Cooper, and John Schrieffer for which they shared the 1972 Nobel Prize.NAVE > FIRST = CARL R., Cooper Pairs, HyperPhysics, Dept. of Physics and Astronomy, Georgia State Univ., 2006,hyperphysics.phy-astr.gsu.edu/Hbase/solids/coop.html, 2008-07-24, Although Cooper pairing is a quantum effect, the reason for the pairing can be seen from a simplified classical explanation.JOURNAL, Spatial Structure of the Cooper PairRelationship to superconductivity
The tendency for all the Cooper pairs in a body to “condense” into the same ground quantum state is responsible for the peculiar properties of superconductivity.Cooper originally considered only the case of an isolated pair’s formation in a metal. When one considers the more realistic state of many electronic pair formations, as is elucidated 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.WEB, Nave, Carl R., The BCS Theory of Superconductivity, HyperPhysics, Dept. of Physics and Astronomy, Georgia State Univ., 2006,hyperphysics.phy-astr.gsu.edu/hbase/solids/bcs.html#c1, 2008-07-24, The gap appears due to many-body effects between electrons feeling the attraction.R. A. Ogg Jr., was first to suggest that electrons might act as pairs coupled by lattice vibrations in the material.JOURNAL, Ogg, Richard A., Bose-Einstein Condensation of Trapped Electron Pairs. Phase Separation and Superconductivity of Metal-Ammonia Solutions, Physical Review, American Physical Society (APS), 69, 5â6, 1 February 1946, 0031-899X, 10.1103/physrev.69.243, 243â244, 1946PhRv...69..243O, Poole Jr, Charles P, “Encyclopedic dictionary of condensed matter physics”, (Academic Press, 2004), p. 576 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 by the theory of Cooper pairing: heavier ions are harder for the electrons to attract and move (how Cooper pairs are formed), which results in smaller binding energy for the pairs.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 electronâexciton interactions or electronâplasmon interactions. Currently, none of these other pairing interactions has been observed in any material.It should be mentioned that Cooper pairing does not involve individual electrons pairing up to form “quasi-bosons”. The paired states are energetically favored, and electrons go in and out of those states preferentially. This is a fine distinction that John Bardeen makes:
“The idea of paired electrons, though not fully accurate, captures the sense of it.“BOOK, Bardeen, John,archive.org/details/cooperativepheno00mott, Cooperative Phenomena, Springer Berlin Heidelberg, 1973, 978-3-642-86005-8, H. Haken and M. Wagner, Berlin, Heidelberg, 67, Electron-Phonon Interactions and Superconductivity, 10.1007/978-3-642-86003-4_6, limited, weblink
The mathematical description of the second-order coherence involved here is given by Yang.JOURNAL, Yang, C. N., Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors, Reviews of Modern Physics, American Physical Society (APS), 34, 4, 1 September 1962, 0034-6861, 10.1103/revmodphys.34.694, 694â704, 1962RvMP...34..694Y, See also
References
{{Reflist}}Further reading
- Michael Tinkham, Introduction to Superconductivity, {{ISBN|0-486-43503-2}}
- Schmidt, Vadim Vasil’evich. The physics of superconductors: Introduction to fundamentals and applications. Springer Science & Business Media, 2013.
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