Generalized Bose-Einstein condensation in superconductivity and superfluidity
- Instituto de Investigaciones en Materiales, Universidad Nacional Autoenoma de Mexico, 04510 Mexico, DF (Mexico)
Unification of the Bardeen, Cooper and Schrieffer (BCS) and the Bose-Einstein condensation (BEC) theories is surveyed in terms of a generalized BEC (GBEC) finite-temperature statistical formalism. A vital distinction is that Cooper pairs (CPs) are true bosons that may suffer a BEC since they obey BE statistics, in contrast with BCS pairs that are 'hard-core bosons' at best. A second crucial ingredient is the explicit presence of hole-pairs (2h) alongside the usual electron-pairs (2e). A third critical element (particularly in 2D where ordinary BEC does not occur) is the linear dispersion relation of CPs in leading order in the center-of-mass momentum (CMM) power-series expansion of the CP energy. The GBEC theory reduces in limiting cases to all five continuum (as opposed to 'spin') statistical theories of superconductivity, from BCS on one extreme to the BEC theory on the other, as well as to the BCS-Bose 'crossover' picture and the 1989 Friedberg-Lee BEC theory. It accounts for 2e- and 2h-CPs in arbitrary proportions while BCS theory can be deduced from the GBEC theory but allows only equal (50%-50%) BE condensed-mixtures of both kinds of CPs. As it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero-temperature condensation energy for all couplings, it suggests that the BCS condensate is a BE condensate of a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly-bound zero-CMM 2e- and 2h-CPs. Without abandoning the electron-phonon mechanism in moderately weak coupling, and fortuituously insensitive to the BF interactions, the GBEC theory suffices to reproduce the unusually high values of T{sub c} (in units of the Fermi temperature T{sub F}) of 0.01-0.05 empirically found in the so-called 'exotic' superconductors of the Uemura plot, including cuprates, in contrast to the low values of T{sub c}/T{sub F}{<=}10{sup -3} roughly reproduced by BCS theory for conventional (mostly elemental) superconductors.
- OSTI ID:
- 21136977
- Journal Information:
- AIP Conference Proceedings, Vol. 994, Issue 1; Conference: 38. Latin-American school of physics ELAF: Quantum information and quantum cold matter, Mexico City (Mexico), 27 Aug - 7 Sep 2007; Other Information: DOI: 10.1063/1.2907757; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
Similar Records
Superconductivity: The persistence of pairs
BEC-driven superconductivity in the cuprates