# Superconducting order parameter of Sr$_2$RuO$_4$: a microscopic perspective

## TL;DR

This paper explores the superconducting order parameter of Sr$_2$RuO$_4$ by incorporating orbital degrees of freedom, revealing a richer classification and proposing a new candidate for the order parameter.

## Contribution

It introduces a detailed orbital-based analysis of the superconducting order parameters in Sr$_2$RuO$_4$, expanding beyond traditional symmetry considerations.

## Key findings

- Orbital degrees of freedom significantly affect the classification of order parameters.
- A new candidate for the superconducting order parameter is proposed.
- The stability and degeneracy of order parameters are analyzed using superconducting fitness.

## Abstract

The character of the superconducting phase of Sr$_2$RuO$_4$, is topic of a longstanding discussion. The classification of the symmetry allowed order parameters has relied on the tetragonal symmetry of the lattice and on cylindrical Fermi surfaces, usually taken to be featureless, not including the non-trivial symmetry aspects related to their orbital content. Here we show how the careful account of the orbital degree of freedom in Sr$_2$RuO$_4$, leads to a much richer classification of order parameters. We analyse the stability and degeneracy of these new order parameters from the perspective of the concept of superconducting fitness and propose a new best order parameter candidate.