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.
Highlights
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
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
Summary
In order to unravel the empirical features of Bi-2212 noted in (28), (29) and (30) in the above framework, we proceed as follows: 1) We first deal with the data in (28) via (33) where, in the latter equation, EF1 is an independent variable If we solve this equation for different assumed values of EF1= ρkθ0 and λm2 = 0, we obtain the corresponding values of λm for pairing via the Ca ions. 2) Since none of the values of λm in Table 1 exceeds the Bogoliubov limit of 0.5, we employ (39) in the 1PEM scenario in order to determine EF2 corresponding to the data in (29) To this end for ρ = 10, for pairing via the Ca ions, we use the following values in (39):. =ρ 10, =λ 0.22043; 2.54 ≤ y ≤ 3.30 4.0226 ×10−4 ≤ q ≤ 5.4521×10−3 , 70 ≥ nu ≥ 7, 9.72 ≥ s ≥ 0.93 1.03×1017 ≤ ns ≤ 1.52 ×1017 , 1.46 ×107 ≥ vc ≥ 9.87 ×106 0.82 ×10−4 ≤ EF 2 ≤ 11.1×10−4 , where the units for ns, vc and EF are cm-3, cm/s and eV, respectively
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