Multipole representation for anisotropic Coulomb interactions

TL;DR

This paper introduces a multipole representation for anisotropic Coulomb interactions in solids, providing a systematic classification based on symmetry and demonstrating its application to SrVO3 and f-electron systems.

Contribution

It proposes a novel multipole framework for anisotropic Coulomb interactions, incorporating symmetry and spatial structure considerations, with practical applications to real materials.

Findings

Few parameters suffice to describe screened Coulomb interactions in SrVO3.

Symmetric A1 component is suppressed in screened interactions but remains dominant in anisotropic parts.

Anisotropic interactions contribute similarly to one-body level splitting in f-electron systems.

Abstract

Multipole representation is proposed for the anisotropic Coulomb interactions in solids. Any local interactions can be expressed as the product of two multipole operators, and the interaction parameters are systematically classified based on the point group symmetry. The form of the multipole interactions are restricted not only by the symmetry and Hermiticity but also by the spatial structure of the interaction, which is closely related to the presence or absence of the odd-rank multipoles. As an exemplary demonstration, the screened Coulomb interaction for SrVO$_3$ is considered, where only a few parameters are necessary for its description. By comparing it with the unscreened version, the totally symmetric $A_1$ representation is found to be strongly suppressed, but the $A_1$ component still gives a dominant contribution for the anisotropic part of the interaction. The anisotropic interactions are also applied to the localized two $f$-electron wave functions, which give the same-order contribution as the one-body level splitting estimated by the band structure calculation.