Thermodynamic properties of superconductors in the extended BCS-Bose crossover theory

Superconductivity in a generalized Bose-Einstein condensation theory (GBEC) is addressed. This theory contains three coupled transcendental equations for all temperatures: two gap-like equations and a particle number density equation that guarantees charge conservation. Here we explore the special case of an extended BCS-Bose crossover picture where two-hole Cooper pairs are explicitly included. We solved these three associated coupled equations yielding two pure Bose-Einstein-condensation phases of two-electron Cooper pairs and/or of two-hole Cooper pairs plus a mixed phase with varying proportions of both kinds of pairs. We found that the mere inclusion of two-hole Cooper pairs can lead to critical temperatures enhanced by several orders of magnitude compared with BCS theory. We also found a weak-intermediate and strong-coupling regime. Within the BCS-Bose crossover theory, we calculated the entropy and from that we analysed the rest of the well-known thermodynamic quantities that can be compared with experimental data. Results fit better for elemental superconductors, suggesting that two-hole Cooper pairs might be indispensable to describe this kind of materials.