Bose-Einstein Condensation in Superconductivity

M. de Llano Instituto de Investigaciones en Materiales UNAM, Mexico City, MEXICO

Bose-Einstein condensation (BEC) theory by Einstein in 1925 based on the work by Bose on photons in 1924 was finally observed in 1995 in laser-cooled magnetically trapped ultra-cold bosonic atomic 87 7 clouds with 37푅푏 nuclei[1]. Within weeks other results quickly followed, initially with 3퐿푖[2] and 23 11푁푎[3]. For a many-fermion system like a superconductor one has electron number-densities of 푛 = 19 23 −3 2 5 10 − 10 푐푚 implying characteristic Fermi temperatures of 푇퐹 = 10 − 10 퐾. On the other hand, an ultra-cold fermionic BECs with enormous average inter-fermion spacings with mass −8 3 −6 densities of 휌 ≃ 10 푔/푐푚 so that 푇퐹 < 10 퐾. Then, one can expect that in the strong-coupling limit one has low densities, or inter-particle spacings much greater than the diameter of composite bosons. Boson-fermion (BF) models[4] of SCs as a BEC go back to the mid-50s, pre-dating even the BCS-Bogoliubov[5] theory. However all BF models neglect the effect of two-hole Cooper pairs (CPs) included on an equal footing with two-electron CPs to give a complete BF model that is a starting point for the recent generalized Bose-Einstein condensation (GBEC)[6] theory. This theory is complete in that it consists of both bosonic CP species coexisting with unbound electrons making it a ternary BF gas instead of the more common binary one.

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