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Statistical Model of Superconductivity in a 2D Binary Boson-Fermion Mixture

M. Casas·N. J. Davidson·M. de Llano·T. A. Mamedov·A. Puente·R. M. Quick·A. Rigo·M. A. Solís
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Abstract

A two-dimensional (2D) assembly of noninteracting, temperature-dependent, composite-boson Cooper pairs (CPs) in chemical and thermal equilibrium with unpaired fermions is examined in a binary boson-fermion statistical model as the superconducting singularity temperature is approached from above. The model is derived from {\it first principles} for the BCS model interfermion interaction from three extrema of the system Helmholtz free energy (subject to constant pairable-fermion number) with respect to: a) the pairable-fermion distribution function; b) the number of excited (bosonic) CPs, i.e., with nonzero total momenta--usually ignored in BCS theory--and with the appropriate (linear, as opposed to quadratic) dispersion relation that arises from the Fermi sea; and c) the number of CPs with zero total momenta. Compared with the BCS theory condensate, higher singularity temperatures for the Bose-Einstein condensate are obtained in the binary boson-fermion mixture model which are in rough agreement with empirical critical temperatures for quasi-2D superconductors

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M. Casas, N. J. Davidson, M. de Llano, T. A. Mamedov, A. Puente, R. M. Quick, A. Rigo, M. A. Solís. 2000-12-11. Statistical Model of Superconductivity in a 2D Binary Boson-Fermion Mixture. https://doi.org/10.1016/s0378-4371(01)00139-x

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