A Fermi Energy-Incorporated Framework for Dealing with the Temperature- and Magnetic Field-Dependent Critical Current Densities of Superconductors and Its Application to Bi-2212

Abstract

It is well known that the critical current density of a superconductor depends on its size, shape, nature of doping and the manner of preparation. It is suggested here that the collective effect of such differences for different samples of the same superconductor is to endow them with different values of the Fermi energy—a single property to which may be attributed the observed variation in their critical current densities. The study reported here extends our earlier work concerned with the generalized BCS equations [Malik, G.P. (2010) Physica B, 405 , 3475-3481; Malik, G.P. (2013) WJCMP, 3 ,103-110]. We develop here for the first time a framework of microscopic equations that incorporates all of the following parameters of a superconductor: temperature, momentum of Cooper pairs, Fermi energy, applied magnetic field and critical current density. As an application of this framework, we address the different values of critical current densities of Bi-2212 for non-zero values of temperature and applied magnetic field that have been reported in the literature.