A New Microscopic Approach To Deal with the Temperature- and Applied Magnetic Field–Dependent Critical Current Densities of Superconductors

Abstract

Based on the formalism of the Bethe-Salpeter equation, we present here a new approach to deal with the temperature (T)- and the applied magnetic field (H)-dependent critical current densities (j_cs) of superconductors (SCs). Saliently, it employs (i) the premise that the chemical potential μ (T, H) subsumes most of the factors to which the widely varying empirical values of j_c (T, H) of an SC are conventionally attributed, (ii) the basic equation that defines j_c as a product of the electronic charge, the number density of superconducting electrons (n_s) and their critical velocity (v_c), (iii) a recently derived equation for n_s (T, H), and (iv) the empirical values of j_c (T, H)—which it is meant to explain—as inputs into one of its equations which, paradoxical though it may seem, is shown to have the virtue of shedding light on several parameters related to j_c (T, H), such as μ, n_s, v_c, m*, n_L, and λ_m, where m* is the effective mass of an electron, n_L the number of occupied Landau levels, and λ_m the magnetic interaction parameter. Remarkably, the approach is found to lead to two branches of μ-dependent solutions with distinctly different values of the parameters corresponding to the same value of j_c (T, H). This is reminiscent of the behavior of the chemical potential in SCs with a low density of charge carriers that was reported by Marel [Physica C 165, 35 (1990)] and described as anomalous. Finally, we show that our approach suggests the exciting possibility of fabricating an SC that has a bespoke value of j_c at suitably chosen values of T and H. For the sake of concreteness, we employ here some of the available empirical data on the j_c (T, H) values of Bi-2212.