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

Gulshan Prakash Malik,Vijaya Shankar Varma

doi:10.4236/wjcmp.2021.113004

Abstract

The empirically reported values of the critical current density (jc) of Bi-2212 as 2.4 × 105 (jc1; Sample 1) and 1.0 × 106 A/cm2 (jc2; Sample 2) are intriguing because both of them correspond to the same values of the temperature T = 4.2 K and the applied magnetic field H = 12 × 104 G. This difference is conventionally attributed to such factors—not all of which are quantifiable—as the geometry, dimensions and the nature of dopants and the manners of preparation of the samples which cause their granular structures, grain boundaries, alignment of the grains and so on to differ. Based on the premise that the chemical potential μ subsumes most of these features, given herein is a novel explanation of the said results in terms of the values of μ of the two samples. This paper revisits the problem that was originally addressed in [Malik G.P., Varma V.S. (2020) WJCMP, 10, 53-70] in the more accurate framework of a subsequent paper [Malik G.P., Varma V.S. (2021) JSNM, 34, 1551-1561]. Besides, it distinguishes between the contributions of the electro-electron (e-e) and the hole-hole (h-h) pairs to jc—a feature to which no heed was paid earlier. The essence of our findings is that the jcs of the two samples differ because they are characterized by different values of the primary variables μi and , where is the effective mass of a charge-carrier and me is the free-electron mass and i = 1 and 2 denote Sample 1 and Sample 2, respectively. In the scenario of the charge-carriers being predominantly h-h pairs, the values of these parameters are estimated to be: μ1 ≈ 12.3 meV, η1 ≈ 0.58; μ2 ≈ 22.7 meV, η2 ≈ 0.94. Following from these and similar estimates when the charge-carriers are e-e pairs, given below for each sample are the detailed results for the values of the secondary variables viz. the number density of the charge-carriers and their critical velocity, the number of occupied Landau levels and the magnetic interaction parameter.

Highlights

Among the family of Bi-based cuprates, Bi2Sr2CaCu2O8 (Bi-2212) and Bi2Sr2Ca2Cu3O10 (Bi-2223) belong to the class of superconductors (SCs) that has the highest values of the critical temperature (Tc), critical magnetic field (Hc) and critical current density
We found that the empirically verifiable values of some of the parameters associated with jc1 or jc2 can be obtained via a consideration of just a few of these triplets
Since we are dealing with the situation where T ≠ 0, H ≠ 0 via Landau quantization prescription (LQP) and values of μ that are not kθ, unsurprisingly, we have found that the two types of carriers, in general, do not make equal contributions

Summary

Introduction

Among the family of Bi-based cuprates, Bi2Sr2CaCu2O8 (Bi-2212) and Bi2Sr2Ca2Cu3O10 (Bi-2223) belong to the class of superconductors (SCs) that has the highest values of the critical temperature (Tc), critical magnetic field (Hc) and critical current density (jc). Employing the formalism of the Bethe-Salpeter equation (BSE), we deal in this paper with two empirical values of jc (T, H), i.e., 2.4 × and 1.0 × A/cm which are intriguing because they have been reported for the same values of T and H, viz T = 4.2 K and H = 12 × 104 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 jc(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. Another remarkable feature of the approach followed in Paper I is that, unlike almost all conventional approaches, it employs directly the basic equation that defines jc(T, H) as the product of the electronic charge e, the number of superconducting charge-carriers ns(T, H) and their critical velocity vc(T, H)

Results

Discussion

Conclusion