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During the last couple of years, research on the enigmatic and canonical unconventional superconductor Sr₂RuO₄ has undergone a renaissance. In particular, new NMR and ultrasound experiments [1,2,3] place considerable constraints on the superconducting order parameter. At the same time, Sr₂RuO₄ is in many respects simple enough that we should be able to understand why and how electrons pair. Superconductivity condenses around 1K from a well-characterized Fermi liquid, and samples are extremely clean.
Here we explore which superconducting order parameters are favorable from the perspective of spin-fluctuation mediated pairing, taking into account the multi-orbital nature of the system and the sizable spin-orbit coupling [4]. We explore the effects of interactions, as well as three-dimensional effects and changes due to strain[5] and compare our proposed superconducting solutions to the available experimental data.

[1] A. Pustogow et al., Nature 574, 72–75 (2019).
[2] Sayak Ghosh et al., Nat. Phys. (2020).
[3] S. Benhabib et al., Nat. Phys. (2020).
[4] A. T. Rømer et al., Phys. Rev. Lett. 123, 247001 (2019).
[5] A. T. Rømer et al., Phys. Rev. B 102, 054506 (2020).