A. Rigo

Cooper pair dispersion relation for weak to strong coupling

Cooper pairing in two dimensions is analyzed with a set of renormalized equations to determine its binding energy for any fermion number density and all coupling assuming a generic pairwise residual interfermion interaction. Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM) and their binding energy is expanded analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent linear term in the CMM dominates the pair excitation energy in weak coupling (also called the BCS regime) while the more familiar quadratic term prevails in strong coupling (the Bose regime). The crossover, though strictly unrelated to BCS theory per se, is studied numerically as it is expected to play a central role in a model of superconductivity as a Bose-Einstein condensation of CPs where the transition temperature vanishes for all dimensionality

Bose-Einstein condensation with a BCS model interaction

dl~2

The Cooper pair dispersion relation

for quadratic dispersion, but is nonzero for all

Two-dimensional Bose-Einstein condensation in cuprate superconductors

dg~1

Linear to quadratic crossover of Cooper-pair dispersion relation

for linear dispersion.

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

Abstract A simple model of a boson-fermion mixture of unpaired fermions plus linear-dispersion-relation Cooper pairs that includes pair-breaking effects leads to Bose-Einstein condensation for dimensions greater than unity, at critical temperatures substantially greater than those of the BCS theory of superconductivity, for the same BCS model interaction between the fermions.

Superconductivity as a Bose-Einstein condensation?

The binding energy of a Cooper pair formed with the BCS model interaction potential is obtained numerically for all coupling in two and three dimensions for all non-zero center-of-mass momentum (CMM) of the pair. The pair breaks up for very small CMM, at most about four orders of magnitude smaller than the maximum CMM allowed by the BCS model interaction, and its binding energy is remarkably linear over the entire range of the CMM up to breakup.

Cooper pair dispersion relation in two dimensions

Abstract A binary gas of noninteracting, temperature-dependent Cooper pairs in chemical/thermal equilibrium with unpaired fermions is studied in a two-dimensional (2D) boson-fermion statistical model analogous to an atom plus diatomic-molecule system. The model naturally suggests a more convenient definition for the bosonic chemical potential whereby access into the degenerate Fermi region of positive fermion chemical potential is now possible. The linear (as opposed to quadratic) dispersion relation of the pairs yields substantially higher T c s than with BCS or pure-boson Bose-Einstein condensation theories, and fall within the range of empirical T c s for quasi-2D copper oxide superconductors.

Pre-formed Cooper pairs and Bose–Einstein condensation in cuprate superconductors

Abstract Cooper pairing is studied in three dimensions to determine its binding energy for all coupling using a general separable interfermion interaction. Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM). A coupling-independent linear term in the CMM dominates the pair excitation energy in weak coupling and/or high fermion density, while the more familiar quadratic term prevails only in the extreme low-density (i.e., vacuum) limit for any nonzero coupling. The linear-to-quadratic crossover of the CP dispersion relation is analyzed numerically, and is expected to play a central role in a model of superconductivity (and superfluidity) simultaneously accommodating a Bardeen–Cooper–Schrieffer condensate as well as a Bose–Einstein condensate of CP bosons.

BEC-DRIVEN SUPERCONDUCTIVITY IN THE CUPRATES

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.