A Study of Heavy-Fermion Superconductors via BCS Equations Incorporating Chemical Potential

Abstract

Heavy-fermion superconductors (HFSCs) are regarded as outside the purview of BCS theory because it is usually constrained by the inequality , where E F , μ , k B , and θ D 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 T c and the gap Δ 0 at T = 0. Further, when μ < k B θ D , we curtail the limits of the equations for T c and Δ 0 to avoid complex-valued solutions. The resulting equations are applied to a prominent member of the HFSC family, i.e ., CeCoIn 5 , 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 T c 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 < k B θ D ; 3) the ( μ , λ ) values obtained in 2) lead to reasonable results for the range of each of the following variables: Δ 0 , 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.