BEC, BCS and BCS-Bose Crossover Theories in Superconductors and Superfluids

TL;DR

This paper explores the BCS-Bose crossover in superconductors and superfluids, revealing the necessity of unphysically large couplings for crossover temperatures and analyzing the implications of simplified models on condensation energy and gap equations.

Contribution

It demonstrates how crossover temperatures require large couplings and clarifies the effects of model simplifications on the BCS gap and condensation energy in superconductors and superfluids.

Findings

Crossover temperatures need unphysically large couplings.

Only half the zero-temperature condensation energy is obtained.

The BCS gap equation is valid for all temperatures.

Abstract

For the Cooper/BCS model interaction in superconductors (SCs) it is shown: a) how BCS-Bose crossover picture transition temperatures Tc, defined self-consistently by both the gap and fermion-number equations, require unphysically large couplings to differ significantly from the Tc of ordinary BCS theory defined without the number equation since here the chemical potential is assumed equal to the Fermi energy; how although ignoring either hole- or electron-Cooper-pairs in the recent "complete boson-fermion model": b) one obtains the precise BCS gap equation for all temperatures T, but c) only half the zero-temperature BCS condensation energy emerges. Results (b) and (c) are also expected to hold for neutral-fermion superfluids (SFs)--such as liquid $^3$He, neutron matter and trapped ultra-cold fermion atomic gases--where the pair-forming two-fermion interaction of course differs from the Cooper/BCS one for SCs.