Microscopic Approach to Magnetism and Superconductivity of $f$-Electron Systems with Filled Skutterudite Structure

TL;DR

This paper uses a microscopic multiorbital Anderson model and NRG analysis to understand the magnetic and superconducting properties of filled skutterudite $f$-electron systems, revealing conditions for enhanced superconductivity.

Contribution

It introduces a simplified $j$-$j$ coupling scheme-based model and investigates the mechanism of superconductivity in filled skutterudites using a two-site Hubbard model.

Findings

Enhanced off-site Cooper pair susceptibility near singlet-triplet transition

Analysis of magnetic susceptibility and entropy across $f$-electron fillings

Identification of conditions favoring superconductivity in skutterudite systems

Abstract

In order to gain a deep insight into $f$-electron properties of filled skutterudite compounds from a microscopic viewpoint, we investigate the multiorbital Anderson model including Coulomb interactions, spin-orbit coupling, and crystalline electric field effect. For each case of $n$=1$\sim$13, where $n$ is the number of $f$ electrons per rare-earth ion, the model is analyzed by using the numerical renormalization group (NRG) method to evaluate magnetic susceptibility and entropy of $f$ electron. In order to make further step to construct a simplified model which can be treated even in a periodic system, we also analyze the Anderson model constructed based on the $j$-$j$ coupling scheme by using the NRG method. Then, we construct an orbital degenerate Hubbard model based on the $j$-$j$ coupling scheme to investigate the mechanism of superconductivity of filled skutterudites. In the 2-site model, we carefully evaluate the superconducting pair susceptibility for the case of $n$=2 and find that the susceptibility for off-site Cooper pair is clearly enhanced only in a transition region in which the singlet and triplet ground states are interchanged.