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 ₂ ) and Three Cuprates (YBCO, Bi-2212 and Tl-2212)

Abstract

Fermi energies (E _Fs) of high- T _c superconductors (SCs) have of late been evincing considerable interest because they are believed to be the cause of their high T _cs 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 _F/ k θ > > 1 (k = Boltzmann constant, θ = Debye temperature), they cannot shed light on the E _Fs of these SCs. This fact leads us to address the gaps (Δ₀s) and T _cs of both types of SCs via recently derived equations which incorporate E _F as a variable. For the specification of the E _F of any SC, we now need another of its properties. Choosing j 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 ₀ that depend solely on the following properties of the SC: E _F, θ, gram-atomic volume, electronic specific heat constant and a dimensionless construct $y=k\theta \sqrt {2m\ast } \text {/}P_{\text {0}} \sqrt {E_{\mathrm {F}} } \text {,}$ where m* is the effective mass of superconducting electrons and P ₀ their critical momentum. Appeal to the experimental values of Δ₀, T _c and j ₀ of any SC then not only leads to values of E _F, m* and P ₀ but also provides plausible clues about how its j ₀—and therefore T _c—may be increased.