Statistical model of superconductivity in a 2D binary boson-fermion mixture

A two-dimensional (2D) assembly of noninteracring, temperature-dependent, c omposite-boson Cooper pairs (CPs) in chemical and thermal equilibrium with unpaired fermions is examined in a binary boson-fermion statistical model a s the superconducting singularity temperature is approached from above. The model is derived from first principles for the BCS model inter-fermion int eraction from three extrema of the system Helmholtz free energy (subject to constant pairable-fermion number) with respect to: (a) the pairable-fermio n distribution function; (b) the number of excited (bosonic) CPs, i.e., wit h nonzero total momenta-usually ignored in BCS theory-and with the appropri ate (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 Bos e-Einstein condensate are obtained in the binary boson-fermion mixture mode l which are in rough agreement with empirical critical temperatures for qua si-2D superconductors. (C) 2001 Elsevier Science B.V. All rights reserved.