Eliashberg theory of superconductivity and inelastic rare-earth impurity scattering in the filled skutteruditeLa1−xPrxOs4Sb12

Abstract

We study the influence of inelastic rare-earth impurity scattering on electron-phonon-mediated superconductivity and mass renormalization in $({\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Pr}}_{x}){\mathrm{Os}}_{4}{\mathrm{Sb}}_{12}$ compounds. Solving the strong-coupling Eliashberg equations we find that the dominant quadrupolar component of the inelastic scattering on Pr impurities yields an enhancement of the superconducting transition temperature ${T}_{c}$ in ${\mathrm{LaOs}}_{4}{\mathrm{Sb}}_{12}$ and increases monotonically as a function of Pr concentration. The calculated results are in good agreement with the experimentally observed ${T}_{c}(x)$ dependence. Our analysis suggests that phonons and quadrupolar excitations cause an attractive electron interaction which results in the formation of Cooper pairs and singlet superconductivity in ${\mathrm{PrOs}}_{4}{\mathrm{Sb}}_{12}$.