A Generalized Bose–Einstein Condensation Theory of Superconductivity Inspired by Bogolyubov

• Main Authors: De Llano, M., Tolmachev, V.V.
• Format: Article
• Language: English
• Published: Відділення фізики і астрономії НАН України 2010
• Subjects: Тверде тіло
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/13288

We survey the unification of the Bardeen, Cooper, Schrieffer (BCS) and the Bose–Einstein condensation (BEC) theories via a generalized BEC (GBEC) formalism. The GBEC describes a ternary boson-fermion gas mixture consisting of fermion-particle- as well as fermion-hole-Cooper-pairs (CPs) that are bosons in thermal and chemical equilibrium with unpaired electrons. One then switches on an interaction Hamiltonian (Hint) that is reminiscent of the single-vertex Fr¨ohlich “two-fermion/one-boson” interaction. In contrast with the well-known BCS “four-fermion” two-vertex Hint, the full GBEC H H0 + Hint is exactly diagonalized with a Bogolyubov–Valatin transformation provided only that one ignores nonzero-total-momenta CPs in the interaction Hint although not in the unperturbed H0 that describes an ideal ternary gas. Nonzerototal-momenta CPs are completely ignored in the full BCS H. Exact diagonalization is possible since the reduced GBEC H becomes bilinear in the fermion creation/annihilation operators on applying the Bogolyubov “recipe” of replacing the remaining zero-totalmomenta boson hole- and particle-CP operators by the square root of their respective temperature- and coupling-dependent boson cnumbers. The resulting GBEC theory subsumes all five statistical theories of superconductors, including the Friedberg–T.D. Lee (1989) BEC theory, and yields hundredfold enhancements in predicted Tcs when compared with BCS predictions with the same two-electron BCS model phonon interaction producing the CPs.