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 [

An Inquiry into Two Intriguing Values of the Critical Current Density of Bi-2212

“…Employing the formalism of the Bethe-Salpeter equation (BSE), we deal in this paper with two empirical values of j c (T, H), i.e., 2.4 × 10 5 and 1.0 × 10 6 A/cm 2 which are intriguing because they have been reported for the same values of T and H, viz T = 4.2 K and H = 12 × 10 4 G [1]. This is a problem that we had earlier addressed in [2]-Paper I hereafter, based on the novel premise that the chemical potential (μ) of an SC subsumes most of the features to which its widely varying values of j c (T, H) are conventionally attributed-features such as its geometry (wire, tape, thin film, etc.) and dimensions, the type of dopants it contains, and the manner of its preparation which causes different samples of it to be characterized by different granular structures and grain boundaries, alignment of the grains and so on, see e.g., [3], most of which are not quantifiable.…”