# Exotic Cooper pairing in multi-orbital models of Sr$_2$RuO$_4$

## TL;DR

This paper explores the complex superconducting pairing mechanisms in Sr$_2$RuO$_4$ by analyzing multi-orbital models, revealing exotic Cooper pairs and the influence of spin-orbit coupling, offering new insights into its unconventional superconductivity.

## Contribution

It introduces a multi-orbital framework to classify and analyze exotic Cooper pairings in Sr$_2$RuO$_4$, highlighting the role of orbital symmetry and spin-orbit coupling.

## Key findings

- Identification of novel orbital-dependent pairing symmetries
- Spin-orbit coupling entangles spin-triplet and singlet pairings
- Extension of classification to three-orbital models

## Abstract

The unconventional superconductivity in Sr$_2$RuO$_4$ continues to defy a unified interpretation. In this paper, we focus on some novel aspects of its superconducting pairing by exploiting the orbital degree of freedom in this material. The multi-orbital nature, combined with the symmetry of the orbitals involved, leads to a plethora of exotic Cooper pairings not accessible in single-orbital systems. Essential physics is illustrated first using a two-orbital model with $d_{xz}$- and $d_{yz}$-orbitals. We classify the gap functions according to the underlying lattice symmetries, analyze the effective theories of a few representative pairings, and make connections to Sr$_2$RuO$_4$ in the course. In particular, we show how spin-orbit coupling may entangle spin-triplet and spin-singlet pairings. For completeness, the classification is generalized to the three-orbital model involving the $d_{xy}$-orbital as well. The orbital-basis approach distinguishes from the itinerant-band description for Sr$_2$RuO$_4$, and hence offers an alternative perspective to investigate its enigmatic superconducting state.