Multipole as $f$-Electron Spin-Charge Density in Filled Skutterudites

TL;DR

This paper defines $f$-electron multipoles as spin-charge densities using tensor operators, enabling microscopic analysis of multipole states in filled skutterudites via linear response theory and numerical renormalization group methods.

Contribution

It introduces a new microscopic definition of $f$-electron multipoles as spin-charge densities, facilitating the analysis of multipole states in filled skutterudites.

Findings

Identification of possible multipole states in filled skutterudite compounds

Application of linear response theory to multipole susceptibility

Numerical analysis using the impurity Anderson model and NRG

Abstract

It is shown that $f$-electron multipole is naturally defined as spin-charge one-electron density operator in the second-quantized form with the use of tensor operator on the analogy of multipole expansion of electromagnetic potential from charge distribution in electromagnetism. Due to this definition of multipole, it is possible to determine multipole state from a microscopic viewpoint on the basis of the standard linear response theory for multipole susceptibility. In order to discuss multipole properties of filled skutterudites, we analyze a seven-orbital impurity Anderson model by employing a numerical renormalization group method. We show our results on possible multipole states of filled skutterudite compounds.