A Boson–Fermion theory that goes beyond the BCS approximations for superconductors

An analysis is given of the effects of common and recurring approximations used in conventional superconductivity theories on the condensation energy values. These approximations come from using the density of states N(ε) and the chemical potential μ(T) either constant or temperature-dependent, respectively. We use three approximations to calculate the critical temperature T_c, the superconductor energy gap Δ(T), the chemical potential μ(T) and the thermodynamic potential Ω(T) which are needed to obtain the condensation energy, and compare them with the exact case, i.e., where no approximations are used. To do this, we use a ternary Boson–Fermion theory of superconductivity composed of unbound electrons (or holes) as fermions plus two-electron and two-hole Cooper pairs, both as bosons. Although all these approximations lead to reasonable values of T_c and Δ(T), the resulting thermodynamic and chemical potentials are quite different, so that the condensation energy value could be incorrect. When N(ε) and μ(T) variables are used, together with a correct physical interpretation of the condensation energy as the sum of the thermodynamic and chemical potential differences, it leads to a better agreement with reported experimental data.

We thank support from grant DGAPA-PAPIIT-UNAM IN114523.