Generalized Cooper pairing and Bose-Einstein condensation

TL;DR

This paper develops a Bethe-Salpeter approach to Cooper pairs based on the BCS ground state, revealing their positive-energy resonances with linear dispersion, which allows Bose-Einstein condensation in two dimensions.

Contribution

It introduces a novel treatment of Cooper pairs that accounts for their finite lifetime and linear dispersion, enabling BEC in 2D, unlike previous quadratic models.

Findings

Cooper pairs can be described as positive-energy resonances with finite lifetime.

Linear dispersion of pairs allows Bose-Einstein condensation in two dimensions.

Traditional models with quadratic dispersion do not support BEC in 2D.

Abstract

A Bethe-Salpeter treatment of Cooper pairs (CPs) based on an ideal Fermi gas (IFG) "sea"' yields the familiar negative-energy, two-particle bound-state if two-hole CPs are ignored, but is meaningless otherwise as it gives purely-imaginary energies. However, when based on the BCS ground state, legitimate two-particle "moving" CPs emerge but as positive-energy, finite-lifetime resonances for nonzero center-of-mass momentum, with a \textit{linear}dispersion leading term. Bose-Einstein condensation of such pairs may thus occur in exactly two dimensions as it cannot with quadratic dispersion.