Eliashberg theory of superconductivity and inelastic rare-earth impurity scattering in filled skutterudite La$_{1-x}$Pr$_{x}$Os$_{4}$Sb$_{12}$

TL;DR

This paper uses Eliashberg theory to analyze how inelastic rare-earth impurity scattering, especially quadrupolar interactions, influences superconductivity in filled skutterudite compounds, explaining experimental T_c trends.

Contribution

It demonstrates that quadrupolar impurity scattering enhances T_c in LaOs$_{4}$Sb$_{12}$ and explains the role of phonons and quadrupolar excitations in pairing mechanisms.

Findings

Quadrupolar impurity scattering increases T_c with Pr concentration.

Theoretical T_c(x) matches experimental data.

Phonons and quadrupolar excitations drive Cooper pairing.

Abstract

We study the influence of inelastic rare-earth impurity scattering on electron-phonon mediated superconductivity and mass renormalization in (La$_{1-x}$Pr$_{x}$)Os$_{4}$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 LaOs$_{4}$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 the attractive electron interaction which results in the formation of Cooper pairs and singlet superconductivity in PrOs$_{4}$Sb$_{12}$.