On the Role of Fermi Energy in Determining Properties of Superconductors: a Detailed Comparative Study of Two Elemental Superconductors (Sn and Pb), a Non-cuprate (MgB{sub 2}) and Three Cuprates (YBCO, Bi-2212 and Tl-2212)
Fermi energies (E{sub F}s) of high- T{sub c} superconductors (SCs) have of late been evincing considerable interest because they are believed to be the cause of their high T{sub c}s and gap structures. Since Bardeen-Cooper-Schrieffer (BCS) equations for elemental and generalized-BCS equations for non-elemental SCs are derived under the blanket of the assumption E{sub F}/ kθ > > 1 (k = Boltzmann constant, θ = Debye temperature), they cannot shed light on the E{sub F}s of these SCs. This fact leads us to address the gaps (Δ{sub 0}s) and T{sub c}s of both types of SCs via recently derived equations which incorporate E{sub F} as a variable. For the specification of the E{sub F} of any SC, we now need another of its properties. Choosing j{sub 0}, the critical current density of the SC at T = 0, and following an idea due to Pines, we present for both types of SCs new equations for j{sub 0} that depend solely on the following properties of the SC: E{sub F}, θ, gram-atomic volume, electronic specific heat constant and a dimensionless construct y=kθ√(2m∗)/P{sub 0}√(E{sub F}), where m* is the effective mass of superconducting electrons and P{sub 0} their critical momentum. Appeal to the experimental values of Δ{sub 0}, T{sub c} and j{sub 0} of any SC then not only leads to values of E{sub F}, m* and P{sub 0} but also provides plausible clues about how its j{sub 0}—and therefore T{sub c}—may be increased.