On a New Number Equation Incorporating Both Temperature and Applied Magnetic Field and Its Application to MgB 2
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ORIGINAL PAPER
On a New Number Equation Incorporating Both Temperature and Applied Magnetic Field and Its Application to MgB2 G. P. Malik 1,2 & V. S. Varma 3,4 Received: 3 July 2020 / Accepted: 6 August 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Guided by recent studies that point to the pivotal role played by the Fermi energy (EF) in determining the properties of hightemperature 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. Keywords High-temperature superconductors . Temperature- and applied magnetic field-dependent critical current density . Number density . Landau quantization . MgB2
1 Introduction It has been known for a long time that the critical temperature (Tc) of some superconductors (SCs)—SrTiO3 being a prime example [1]—depends in a marked manner on the density of charge carriers (ns). Recent studies also suggest that low values of the Fermi energy (EF) (which is related to ns) play a pivotal role in determining the properties of high-Tc SCs (see, e.g., [2–4]). Guided by these considerations, we have been following an approach based on the generalized BCS equations (GBCSEs), which are derived from a parent Bethe-Salpeter equation, where the Tc, gaps (Δs), critical applied field (Hc), and the critical current density (jc) of both
* G. P. Malik [email protected]; [email protected] V. S. Varma [email protected] 1
B-208 Sushant Lok 1, Gurugram, Haryana, India
2
(Formerly) Theory Group, School of Environmental Sciences, Jawaharlal Nehru University, New Delhi, India
3
180 Mall Apartments, Mall Road, Delhi, India
4
(Formerly) Department of Physics and Astrophysics, University of Delhi, Delhi, India
elemental and composite SCs are explicitly dependent on EF, leading to a unified framework to deal with all of these quantities in terms of the Debye temperature (θ) of the SC (and the θ values of its constituents for a composite SC) and one or more interaction parameters (λs). Initiated in [5] (see also [6] for a correction) to deal with jc (T = 0, H = 0), the approach was followed up in several papers—for references to these, see a recent review [7]—for different SCs for nonzero values of T and H. This differs from the usual approach where (i) equations for the Tcs and the Δs of an SC are independent of EF because of the assumption that EF > > k θ, where k is the Boltzmann constant,
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