Author(s)

G. P. Malik^*

Theory Group, School of Environmental Sciences, Jawaharlal Nehru University, New Delhi, India.

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 Δ₀ at T = 0. Further, when μ < k_Bθ_D, we curtail the limits of the equations for T_c 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 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_Bθ_D; 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.

Range of Application of the BCS Theory, Incorporation of Chemical Potential into Equations for T_c 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

Malik, G. (2015) A Study of Heavy-Fermion Superconductors via BCS Equations Incorporating Chemical Potential. Journal of Modern Physics, 6, 1233-1242. doi: 10.4236/jmp.2015.69128.