A Detailed Study of the Role of Fermi Energy in Determining Properties of Superconducting NbN

Abstract

The recent concern with the role of Fermi energy ( E F ) as a determinant of the properties of a superconductor (SC) led us to present new E F -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 T c s 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 E F -dependent, it employed an equation for the dimensionless construct that depends on E F 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 E F -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.