On a New Number Equation Incorporating Both Temperature and Applied Magnetic Field and Its Application to MgB2

Abstract

Guided by recent studies that point to the pivotal role played by the Fermi energy (EF) in determining the properties of high-temperature superconductors, we have been following a course where the critical temperature, gap(s), and the temperature T- and the applied magnetic field H-dependent critical current density jc (T, H) are addressed in a unified, EF-incorporated framework. Needed in such an approach is an equation for the number density ns (T, H) which is a constituent of jc (T, H). This equation is derived here by applying the field-theoretic Landau quantization prescription to ns (T, H = 0). As an application of the new equation, we also deal herein with a few empirical values of jc (T, H) of MgB2 and show that the corresponding ns (T, H) values lead to bounds on the effective mass of the charge carriers, the Fermi velocity, and the critical velocity.