# Superconducting order of $\mathrm{Sr}_2\mathrm{RuO}_4$ from a three-dimensional microscopic model

## TL;DR

This study uses a detailed three-dimensional microscopic model to analyze the superconducting order parameters of Sr2RuO4, revealing the favored pairing symmetries depending on Hund's coupling and their consistency with experimental data.

## Contribution

It provides a comprehensive microscopic analysis of Sr2RuO4's superconducting states, highlighting the influence of Hund's coupling on pairing symmetry and reconciling theoretical orders with experimental observations.

## Key findings

- Odd-parity helical order favored at smaller Hund's coupling.
- Even-parity d-wave order favored at larger Hund's coupling.
- Chiral p-wave order conflicts with NMR data.

## Abstract

We compute and compare even- and odd-parity superconducting order parameters of strontium ruthenate ($\mathrm{Sr}_2\mathrm{RuO}_4$) in the limit of weak interactions, resulting from a fully microscopic three-dimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity $d$-wave order are favored for smaller and larger values of the Hund's coupling parameter $J$, respectively. Both orders are found compatible with specific heat data and the recently-reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al. Nature 574, 72 (2019)]. The chiral $p$-wave order, numerically very competitive with helical order, sharply conflicts with the NMR experiment.