Is BCS Related with BEC?
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We present the complete phase diagram implied by the generalized Bose-Einstein condensation (GBEC) formalism that in essence is a ternary boson-fermion (BF) model with three constituents: two bosonic [two-electron Cooper pairs (2e-CPs) and two-hole Cooper pairs (2h-CPs)] along with unpaired electrons whose number naturally vanishes in the limit of infinite e-e coupling. There arise three coupled transcendental equations to be solved self-consistently: two gap-like equations (one for each kind of CPs) and a third which guarantees charge conservation via the number equation for the total electron number density of the system. The unknown variables are the chemical potential as well as the number density of zero-momentum 2e-CPs and 2h-CPs, each depending on coupling as well as absolute temperature. The GBEC subsumes as special cases all statistical theories of superconductors including BCS and BEC. It also subsumes the BCS-Bose “crossover” theory which in turn relates BCS with BEC. The GBEC formalism yields a substantial increase in critical temperature compared with BCS theory even with only electron-phonon dynamics.
KeywordsGeneralized Bose-Einstein Condensation High-Tc superconductors BCS theory Cooper pairs
IC thanks CONACyT-Mexico for the postgraduate grant 260978 and MG and MdeLl thank PAPIIT-UNAM-Mexico for grants IN116914 and IN100314, respectively.
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