Superconductor superfluid density from the Bardeen-Cooper-Schrieffer/Bose crossover theory

The superfluid density n(s) (T) of a superconductor is calculated based on the generalized Bose-Einstein condensation (GBEC) theory that addresses a fully-interacting ternary boson-fermion gas mixture of free electrons as fermions, plus twoelectron Cooper pairs (2eCPs) and also, explicitly, two-hole Cooper pairs (2hCPs), both as bosons. Here we consider two special cases (i) 100%-0% (i.e., with no condensed 2hCPs) and (ii) 0%-100% (i.e., with no condensed 2eCPs). Subsumed in GBEC are the Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) theories along with the BCS-BEC crossover theory extended with 2hCPs. We find that in the weak-coupling regime n(s)(0) agrees with data from the Uemura et al. (2004) graph for several elemental SCs by taking in 3D with a quadratic energy-dispersion relation while in 2D with a linear relation are much too far below the data. In the strong-coupling regime the linear behavior of critical temperature T-c vs n(s) (0) obtained here is just as BoZovk et al. (2016) found. However, in 2D with a linear relation accounting for 0%-100%, n(s) (T)/n(s) (0) compares well with some high-T-c -cuprate SC data between the two coupling regimes.

Automated summary

The superfluid density of a superconductor is calculated using the generalized Bose-Einstein condensation theory, considering two special cases. The results show a linear relationship between temperature and superfluid density in the strong-coupling regime, while in the weak-coupling regime, the results agree with experimental data.