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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
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that make up the rigid lattice of the metal. This attraction distorts the ion lattice, moving the ions slightly toward the electron, increasing the positive charge density of the lattice in the vicinity. This positive charge can attract other electrons. At long distances, this attraction between
239:
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:
224:) 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.
227:
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
119:
electrons due to the displaced ions can overcome the electrons' repulsion due to their negative charge, and cause them to pair up. The rigorous quantum mechanical explanation shows that the effect is due to
170:
are symmetric under particle interchange. Therefore, unlike electrons, multiple Cooper pairs are allowed to be in the same quantum state, which is responsible for the phenomenon of superconductivity.
213:
leads to superconductivity, since small excitations such as scattering of electrons are forbidden. The gap appears due to many-body effects between electrons feeling the attraction.
134:, and thermal energy can easily break the pairs. So only at low temperatures, in metal and other substrates, are a significant number of the electrons bound in Cooper pairs.
1188:
540:
Ogg, Richard A. (1 February 1946). "Bose-Einstein
Condensation of Trapped Electron Pairs. Phase Separation and Superconductivity of Metal-Ammonia Solutions".
698:
Schmidt, Vadim Vasil'evich. The physics of superconductors: Introduction to fundamentals and applications. Springer
Science & Business Media, 2013.
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apart. This distance is usually greater than the average interelectron distance so that many Cooper pairs can occupy the same space. Electrons have
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The electrons in a pair are not necessarily close together; because the interaction is long range, paired electrons may still be many hundreds of
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R. A. Ogg Jr., was first to suggest that electrons might act as pairs coupled by lattice vibrations in the material. This was indicated by the
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Although Cooper pairing is a quantum effect, the reason for the pairing can be seen from a simplified classical explanation. An electron in a
1181:
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635:
Yang, C. N. (1 September 1962). "Concept of Off-Diagonal Long-Range Order and the
Quantum Phases of Liquid He and of Superconductors".
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Bardeen, John (1973). "Electron-Phonon
Interactions and Superconductivity". In H. Haken and M. Wagner (ed.).
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the electrons, meaning that all excitations of the system must possess some minimum amount of energy. This
582:
Poole Jr, Charles P, "Encyclopedic dictionary of condensed matter physics", (Academic Press, 2004), p. 576
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effect observed in superconductors. The isotope effect showed that materials with heavier ions (different
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interactions. Currently, none of these other pairing interactions has been observed in any material.
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interactions, with the phonon being the collective motion of the positively-charged lattice.
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interaction. The Cooper pair state is responsible for superconductivity, as described in the
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The mathematical description of the second-order coherence involved here is given by Yang.
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Pair of electrons bound together at low temperature, allowing for superconductivity
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The energy of the pairing interaction is quite weak, of the order of 10
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Cooper showed that an arbitrarily small attraction between electrons in a
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of helium-3 at low temperatures. In 2008 it was proposed that pairs of
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110:. The electron is repelled from other electrons due to their negative
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can cause a paired state of electrons to have a lower energy than the
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The BCS theory is also applicable to other fermion systems, such as
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in a certain manner first described in 1956 by
American physicist
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is responsible for the peculiar properties of superconductivity.
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Kadin, Alan M. (2005). "Spatial
Structure of the Cooper Pair".
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Feynman, Richard P.; Leighton, Robert; Sands, Matthew (1965).
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600:. Berlin, Heidelberg: Springer Berlin Heidelberg. p.
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67:, which implies that the pair is bound. In conventional
522:. Dept. of Physics and Astronomy, Georgia State Univ
350:. Dept. of Physics and Astronomy, Georgia State Univ
197:
The tendency for all the Cooper pairs in a body to "
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413:Fujita, Shigeji; Ito, Kei; Godoy, Salvador (2009).
548:(5–6). American Physical Society (APS): 243–244.
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370:Journal of Superconductivity and Novel Magnetism
296:"Bound electron pairs in a degenerate Fermi gas"
177:. Indeed, Cooper pairing is responsible for the
162:of a Cooper pair is integer (0 or 1) so it is a
643:(4). American Physical Society (APS): 694–704.
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686:Introduction to Superconductivity
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637:Reviews of Modern Physics
392:10.1007/s10948-006-0198-z
232:interactions or electron–
1598:Bogoliubov quasiparticle
1342:Quantum spin Hall effect
1234:Bose–Einstein condensate
1198:Condensed matter physics
813:London penetration depth
488:"Cooper Pairs of Bosons"
323:10.1103/PhysRev.104.1189
294:Cooper, Leon N. (1956).
21:condensed matter physics
1106:List of superconductors
984:By critical temperature
562:10.1103/physrev.69.243
512:Nave, Carl R. (2006).
340:Nave, Carl R. (2006).
106:normally behaves as a
1474:Topological insulator
1408:Anderson localization
752:Bean's critical state
596:Cooperative Phenomena
1352:Aharonov–Bohm effect
1239:Fermionic condensate
927:By magnetic response
260:Color–flavor locking
203:ground quantum state
43:) bound together at
1743:Physics WikiProject
1418:tight binding model
1398:Fermi liquid theory
1383:Free electron model
1332:Quantum Hall effect
1313:Electrons in solids
879:persistent currents
864:Little–Parks effect
649:1962RvMP...34..694Y
554:1946PhRv...69..243O
423:Springer Publishing
314:1956PhRv..104.1189C
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839:Andreev reflection
834:Abrikosov vortices
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166:. This means the
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854:flux pumping
849:flux pinning
844:Cooper pairs
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1660:Soft matter
1560:Ferromagnet
1378:Drude model
1347:Berry phase
1327:Hall effect
894:SU(2) color
874:Homes's law
462:. pp.
425:. pp.
97:Nobel Prize
89:Leon Cooper
55:Description
49:Leon Cooper
25:Cooper pair
1759:Categories
1575:Spin glass
1570:Metamagnet
1550:Paramagnet
1437:Conduction
1413:BCS theory
1254:Superfluid
1249:Supersolid
1030:iron-based
889:reentrance
526:2008-07-24
498:2009-09-01
354:2008-07-24
281:References
160:total spin
158:, but the
139:nanometers
81:BCS theory
39:(or other
1633:Polariton
1540:Diamagnet
1488:Couplings
1464:Conductor
1459:Semimetal
1444:Insulator
1320:Phenomena
1244:Fermi gas
827:Phenomena
665:0034-6861
570:0031-899X
270:Lone pair
228:electron–
37:electrons
1707:Category
1688:Colloids
1062:cryotron
1020:cuprates
1015:covalent
772:Matthias
740:Theories
400:54948290
254:See also
199:condense
175:helium-3
156:fermions
121:electron
73:electron
41:fermions
29:BCS pair
1719:Commons
1683:Polymer
1650:Polaron
1628:Plasmon
1608:Exciton
1156:more...
1040:organic
645:Bibcode
550:Bibcode
466:–7, 8.
310:Bibcode
234:plasmon
230:exciton
218:isotope
148:⁄
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1613:Magnon
1371:Theory
1229:Plasma
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933:Types
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185:in an
183:bosons
125:phonon
112:charge
91:, and
77:phonon
1593:Anyon
1214:Solid
1146:TBCCO
1118:BSCCO
1097:wires
1092:SQUID
429:–27.
396:S2CID
378:arXiv
143:spin-
104:metal
61:metal
1603:Hole
1151:YBCO
1141:NbTi
1136:NbSn
1123:LBCO
690:ISBN
661:ISSN
614:ISBN
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468:ISBN
431:ISBN
116:ions
23:, a
1224:Gas
1128:MgB
1077:NMR
1072:MRI
947:1.5
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