Cooper pair dispersion relation for weak to strong coupling

Abstract

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)--usually neglected in BCS theory--and their binding energy is expanded analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent {\it 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 {\it 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 $d\le 2$ for quadratic dispersion, but is {\it nonzero} for all $d\ge 1$ for linear dispersion.

11 pages plus 3 figures, revised version accepted in Physical Review B

References in corpus (3)

• From Cooper Pairs to Composite Bosons: A Generalized RPA Analysis of Collective Excitations
• Renormalization in Nonrelativistic Quantum Mechanics
• Universal scaling in BCS superconductivity in three dimensions in non-$s$ waves

Cited by in corpus (15)

• Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
• One-dimensional superfluid Bose-Fermi mixture: mixing, demixing and bright solitons
• The BCS-Bose Crossover Theory
• Superfluid Fermi-Fermi mixture: phase diagram, stability, and soliton formation
• Linear to quadratic crossover of Cooper pair dispersion relation
• Universal behavior of a trapped Fermi superfluid in the BCS-unitarity crossover
• Two-dimensional Bose-Einstein Condensation in Cuprate Superconductors
• Specific heat of underdoped cuprate superconductors from a phenomenological layered Boson-Fermion model
• Polaron and bipolaron dispersion curves in one dimension for intermediate coupling
• Further evidence for linearly-dispersive Cooper pairs
• Pre-formed Cooper pairs and Bose-Einstein condensation in cuprate superconductors
• Bose-Einstein condensation of nonzero-center-of-mass-momentum Cooper pairs
• Stability of condensate in superconductors
• Modification of a charged-Bose-gas model for observed room-temperature superconductivity in narrow channels through films of oxidised atactic polypropylene
• One-dimensional Cooper pairing