Multipole-fluctuation pairing mechanism of $d_{x^2-y^2}+ig$ superconductivity in Sr$_2$RuO$_4$

TL;DR

This paper proposes a theoretical mechanism for the $d_{x^2-y^2}+ig$ superconducting pairing symmetry in Sr$_2$RuO$_4$, based on multipole fluctuations within an Eliashberg framework, aligning with experimental observations.

Contribution

It introduces a phenomenological model combining realistic band structures and multipole fluctuations to explain the emergence of $d_{x^2-y^2}+ig$ pairing in Sr$_2$RuO$_4$.

Findings

$d_{x^2-y^2}+ig$ pairing arises from multipole fluctuations.

Coexistence of antiferromagnetic, ferromagnetic, and electric fluctuations is key.

Model aligns with experimental evidence for pairing symmetry.

Abstract

Despite of many experimental and theoretical efforts, the pairing symmetry of superconductivity in Sr$_2$RuO$_4$ remains undecided. The accidentally degenerate $d_{x^2-y^2}+ig$ is consistent with most current experiments and seems to be one of the most probable candidates, but we still lack a satisfactory theoretical mechanism for its appearance. Here we construct a phenomenological model combining realistic electronic band structures and all symmetry-allowed multipole fluctuations as potential pairing glues, and make a systematic survey of major pairing states within the Eliashberg framework. Our calculations show that $d_{x^2-y^2}+ig$ can arise naturally from the interplay of antiferromagnetic, ferromagnetic, and electric multipole fluctuations whose coexistence is manifested in previous experiments and calculations. Our work provides a physically reasonable basis supporting the possibility of $d_{x^2-y^2}+ig$ pairing in superconducting Sr$_2$RuO$_4$.