Fermi Energy-Incorporated Generalized BCS Equations for the Temperature-Dependent Critical Current Density and the Related Parameters of a Superconductor for All T ≤ Tc and Their Application to Aluminium Strips

Presented here are the Generalized BCS Equations incorporating Fermi Energy for the study of the {Δ, Tc, jc(T)} values of both elemental and composite superconductors (SCs) for all T ≤ Tc, where Δ, Tc and jc(T) denote, respectively, one of the gap values, the critical temperature and the T-dependent critical current density. This framework, which extends our earlier study that dealt with the {Δ₀, Tc, jc(0)} values of an SC, is also shown to lead to T-dependent values of several other related parameters such as the effective mass of electrons, their number density, critical velocity, Fermi velocity (V_F), coherence length and the London penetration depth. The extended framework is applied to the jc(T) data reported by Romijn et al. for superconducting Aluminium strips and is shown not only to provide an alternative to the explanation given by them, but also to some novel features such as the role of the Sommerfeld coefficient γ(T) in the context of jc(T) and the role of V_F(T) in the context of a recent finding by Plumb et al. about the superconductivity of Bi-2212.