Brillouin-Wigner theory of mixed-valence rare-earth impurities in Bardeen-Cooper-Schrieffer superconductors.

Abstract

We present a Brillouin-Wigner-type theory for the mixed-valence rare-earth impurities in Bardeen-Cooper-Schrieffer (BCS) superconductors. The impurity is described by a degenerate Anderson model with two configurations 4${f}^{0}$ and 4${f}^{1}$ in the infinite-correlation limit. Two important quantities characterizing the superconducting state, i.e., the reduced transition temperature ${T}_{c}$/${T}_{c0}$ and the reduced specific-heat jump \ensuremath{\Delta}C/\ensuremath{\Delta}${C}_{0}$, are calculated as functions of the impurity concentration x and the valence of the 4${f}^{1}$ configuration ${n}_{f}$. The ${T}_{c}$/${T}_{c0}$ versus x curves obtained display exponential shapes which become steeper quickly with larger ${n}_{f}$. The \ensuremath{\Delta}C/\ensuremath{\Delta}${C}_{0}$ versus ${T}_{c}$/${T}_{c0}$ curves show upward deviation with respect to the BCS law of corresponding states in contrast to the case of magnetic impurities. The theory is also fitted to the data of dilute superconducting ${\mathrm{Th}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ce}}_{\mathrm{x}}$ alloys with a comparison to a previous Hartree-Fock theory.