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

The empirically reported values of the critical current density (j_c) of Bi-2212 as 2.4 × 10⁵ (j_c1; Sample 1) and 1.0 × 10⁶ A/cm² (j_c2; 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 j_c—a feature to which no heed was paid earlier. The essence of our findings is that the j_cs of the two samples differ because they are characterized by different values of the primary variables μ_i and , where is the effective mass of a charge-carrier and m_e 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.