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

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 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.