Fermi Energy-Incorporated Generalized BCS Equations for the Temperature-Dependent Critical Current Density and the Related Parameters of a Superconductor for All &lt;i&gt;T&lt;/i&gt; ≤ &lt;i&gt;Tc&lt;/i&gt; and Their Application to Aluminium Strips

G P Malik ,Vijayalakshmi Varma

doi:10.4236/wjcmp.2019.93004

Abstract

Presented here are the Generalized BCS Equations incorporating Fermi Energy for the study of the {Δ, Tc, jc(T)} values of both elemental and composite superconductors (SCs) for all T ≤ Tc, where Δ, Tc and jc(T) denote, respectively, one of the gap values, the critical temperature and the T-dependent critical current density. This framework, which extends our earlier study that dealt with the {Δ0, Tc, jc(0)} values of an SC, is also shown to lead to T-dependent values of several other related parameters such as the effective mass of electrons, their number density, critical velocity, Fermi velocity (VF), coherence length and the London penetration depth. The extended framework is applied to the jc(T) data reported by Romijn et al. for superconducting Aluminium strips and is shown not only to provide an alternative to the explanation given by them, but also to some novel features such as the role of the Sommerfeld coefficient γ(T) in the context of jc(T) and the role of VF(T) in the context of a recent finding by Plumb et al. about the superconductivity of Bi-2212.

Highlights

Adopting the framework of the Fermi energy (EF)-incorporated generalized BCS equations (GBCSEs), we deal here with the calculation of the critical current density jc(T)—for all T between 0 and Tc—of a superconductor (SC) which is not subjected to any external magnetic field
In order to provide a perspective of the conceptual basis of the conventional, multi-band approach (MBA) to the study of the set {Δ, Tc, jc(T)} of a composite SC vis-à-vis that of the GBCSEs-based approach, we include an overview of both approaches
Since the data in [1] are explicable in the conventional approach via both the phenomenological Bardeen equation [2] and the Kupriyanov and Lukichev (KL) [3] theory discussed below, the purpose of this paper is to show that the GBCSEs-based approach provides a valuable alternative explanation of the same data

Summary

Introduction

Adopting the framework of the Fermi energy (EF)-incorporated generalized BCS equations (GBCSEs), we deal here with the calculation of the critical current density jc(T)—for all T between 0 and Tc—of a superconductor (SC) which is not subjected to any external magnetic field. Since the data in [1] are explicable in the conventional approach via both the phenomenological Bardeen equation [2] and the Kupriyanov and Lukichev (KL) [3] theory discussed below, the purpose of this paper is to show that the GBCSEs-based approach provides a valuable alternative explanation of the same data. Are given the EF-incorporated GBCSEs in the scenario when a two-phonon exchange mechanism (2 PEM) is operative. These equations provide a unified framework for the description of the set {Δ2, Tc, j0}, where Δ2 is the larger of the two gaps of the SC.

Objectives

Findings

Discussion

Conclusion