Two-Electron and Two-Hole Cooper Pairs in Superconductivity

We revisit the generalized Bose-Einstein condensation (GBEC) theory which addresses a ternary boson-fermion gas including two-hole Cooper pairs (2hCPs) as an essential component in superconductivity. Here, we extend the BCS-Bose crossover theory, itself subsumed in BEC, by explicitly including 2hCPs. Shown here are phase diagrams of T c / T F , where T c is the critical temperature and T F the Fermi temperature and Δ(0)/ E F vs n / n f , where Δ(0) is the energy gap at zero temperature and E F is the Fermi energy of an ideal Fermi gas, with n the total electron number density and n f is that of unbound electrons at zero temperature. These phase diagrams are obtained for two pure phases, one with two-electron Cooper pairs (2eCPs) and the other with 2hCPs, plus a mixed phase with arbitrary proportions of 2e/2hCPs. We find that the extended BCS-Bose crossover predicts T c / T F as well Δ(0)/ E F values for the elemental superconductors (SCs) Al, In, Sn, Pb, Hg, and Nb which compare reasonably well with experimental data.