Extended BCS-Bose Crossover

Applying the generalized Bose-Einstein condensation (GBEC) formalism, we extend the BCS-Bose crossover theory by explicitly including hole Cooper pairs (2hCPs). From this, follows a phase diagram with two pure phases, one with 2hCPs and the other with electron Cooper pairs (2eCPs), plus a mixed phase with arbitrary proportions of 2eCPs and 2hCPs. The special-case phase when there is perfect symmetry, i.e., with ideal 50-50 proportions between 2eCPs and 2hCPs, corresponds to the usual BCS-Bose crossover. Explicitly including 2hCPs yields an extended BCS-Bose crossover which predicts improved T_c/T_F values for some conventional superconductors (i.e., with electron-phonon dynamics) when compared with experiment. To do this, we employ the BCS dimensionless coupling constant λ_BCS via the BCS gap equation and compare with the Bogoliubov et al. upper limit λ_BCS ≤ 1/2. Another phase diagram presented exhibits experimental T_c/T_F values for some conventional superconductors for arbitrary proportions between 2eCPs and 2hCPs as function of Δn = n/n_f − 1, where n is the electron concentration and n_f that of unbound electrons at T = 0. The extended crossover is compared with experimental T_c/T_F values as well as to the gap-to- T_c ratio.