Superconducting Symmetries of Sr$_2$RuO$_4$ from First-Principles Electronic Structure

TL;DR

This study uses first-principles calculations to explore the superconducting pairing symmetries in Sr$_2$RuO$_4$, revealing dominant spin-singlet $d$-wave pairing near magnetic instabilities and possible triplet pairings away from them.

Contribution

It constructs a detailed pairing interaction model based on correlated normal state calculations, identifying potential superconducting symmetries in Sr$_2$RuO$_4$.

Findings

Spin-singlet $d$-wave pairing near magnetic instabilities

Emergence of time-reversal symmetry-breaking triplet pairings away from instabilities

Correlations favor antiferromagnetic over ferromagnetic fluctuations

Abstract

Although correlated electronic-structure calculations explain very well the normal state of Sr$_2$RuO$_4$, its superconducting symmetry is still unknown. Here we construct the spin and charge fluctuation pairing interactions based on its correlated normal state. Correlations significantly reduce ferromagnetic in favor of antiferromagnetic fluctuations and increase inter-orbital pairing. From the normal-state Eliashberg equations, we find spin-singlet $d$-wave pairing close to magnetic instabilities. Away from these instabilities, where charge fluctuations increase, we find two time-reversal symmetry-breaking spin-triplets: an odd-frequency $s$-wave, and a doubly-degenerate inter-orbital pairing between $d_{xy}$ and ($d_{yz},d_{xz}$).