TITLE:
A Study of Heavy-Fermion Superconductors via BCS Equations Incorporating Chemical Potential
AUTHORS:
G. P. Malik
KEYWORDS:
Range of Application of the BCS Theory, Incorporation of Chemical Potential into Equations for Tc and Δ0, Extended BCS Theory, Heavy-Fermion Superconductors, Ratio of the Mass of a Conduction Electron and the Free Electron Mass, Density of Charge Carriers
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.9,
August
10,
2015
ABSTRACT: Heavy-fermion superconductors (HFSCs) are regarded as outside the purview of BCS theory because it is usually constrained by the inequality , where EF, μ, kB, and θD are, respectively, the Fermi energy, chemical potential, Boltzmann constant, and the Debye temperature. We show that this restriction can be removed by incorporating μ into the equations for Tc and the gap Δ0 at T = 0. Further, when μ kBθD, we curtail the limits of the equations for Tc and Δ0 to avoid complex-valued solutions. The resulting equations are applied to a prominent member of the HFSC family, i.e., CeCoIn5, by appealing to ideas due to Born and Karmann, Suhl et al., and Bianconi et al. Since the equations now contain an additional variable μ, we find that 1) the Tc of the SC can be accounted for by a multitude of values of the (μ, λ) pair, λ being the interaction parameter; 2) the λ vs. μ plot has a dome-like structure when μ kBθD; 3) the (μ, λ) values obtained in 2) lead to reasonable results for the range of each of the following variables: Δ0, s, and n, where s is the ratio of the mass of a conduction electron and the free electron mass and n is the number density of charge carriers in the SC.