Abstract
The recent concern with the role of Fermi energy (EF) as a determinant of the properties of a superconductor (SC) led us to present new EF-dependent equations for the effective mass (m*) of superconducting electrons, their critical velocity, number density, and critical current density, and also the results of the calculations of these parameters for six SCs the Tcs of which vary between 3.72 and 110 K. While this work was based on, besides an idea due to Pines, equations for Tc and the gap at T = 0 that are explicitly EF-dependent, it employed an equation for the dimensionless construct that depends on EF only implicitly; k in this equation is the Boltzmann constant, θ is the Debye temperature, and P0 is the critical momentum of Cooper pairs. To meet the demand of consistency, we give here derivation of an equation for y that is also explicitly EF-dependent. The resulting framework is employed to (a) review the previous results for the six SCs noted above and (b) carry out a study of NbN which is the simplest composite SC that can shed further light on our approach. The study of NbN is woven around the primary data of Semenov et al. For the additional required inputs, we appeal to the empirical data of Roedhammer et al. and of Antonova et al.
Highlights
Some of the recent studies [1]-[7] concerned with high-Tc superconductors (SCs) have been motivated by the belief that Fermi energy (EF) plays an important role in determining their Tcs and gap-structures
While this work was based on, besides an idea due to Pines, equations for Tc and the gap at T = 0 that are explicitly EF-dependent, it employed an equation for the dimensionless construct y = kθ 2m * P0 EF that depends on EF only implicitly; k in this equation is the Boltzmann constant, θ is the Debye temperature, and P0 is the critical momentum of Cooper pairs
We note that, based on neutron powder diffraction experiments, different values of Debye temperature for the constituents of anisotropic LCO have been reported [19]. This lends support to the idea that the Debye temperature of a composite SC needs to be “resolved.” The results reported here depend only on the value of θNb, for the identification of which we have employed (34) and (35) as a vehicle
Summary
Some of the recent studies [1]-[7] concerned with high-Tc superconductors (SCs) have been motivated by the belief that Fermi energy (EF) plays an important role in determining their Tcs and gap-structures. These studies make it natural to ask: why not incorporate EF (equivalently, chemical potential μ) into the equations for the Tc and the gap ∆ of an SC, and treat it as an independent variable? While the results of such a study for Sn, Pb, MgB2, YBCO, Bi-2212, and Tl-2212 were reported in [8], it was based on, unlike the equations for ∆0 and Tc, an equation for the dimensionless construct y , defined below, that is dependent on EF only implicitly
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