Generalized Bose–Einstein Condensation in Superconductivity

Abstract

Unification of the BCS and the Bose–Einstein condensation (BEC) theories is surveyed via a generalized BEC (GBEC) finite-temperature statistical formalism. Its major difference with BCS theory is that it can be diagonalized exactly. Under specified conditions it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero-temperature condensation energy for all couplings, thereby suggesting that a BCS condensate is a BE condensate in a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly-bound two-electron and two-hole Cooper pairs. Without abandoning the electron–phonon mechanism in moderately weak coupling it suffices, in principle, to reproduce the unusually high values of T c (in units of the Fermi temperature T F ) of 0.01–0.05 empirically reported in the so-called “exotic” superconductors of the Uemura plot, including cuprates, in contrast to the low values of T c /T F ≤10−3 roughly reproduced by BCS theory for conventional (mostly elemental) superconductors.