The mysterious oddness of strontium ruthenate's superconducting state: Strong electronic correlations and spin-orbit coupling in multi-orbital systems

Recent experimental improvements have established key properties of the superconducting order parameter of strontium ruthenate, yet some of those give seemingly different pictures that are challenging to reconcile in a single theory [1, 2]. First reviewing these latest developments, we then present a numerical framework to study potential leading instabilities based on first-principles approaches and strong electronic correlations [3, 4]. The results highlight the importance of spin-orbit coupling in entangling electronic quantum numbers, yielding rich and complex order parameters. They suggest a rare type of order dominated by odd-frequency pairing as a prime candidate, which is also found using frequency-dependent linear response theory within dynamical mean-field theory. We discuss observable signatures in specific heat associated with these leading states and develop a static interpretation of odd-frequency pairings.

[1] Li et al., Proceedings of the National Academy of Sciences 118, e2020492118 (2021).

[2] Grinenko et al., Nature Physics 17, 748 (2021).

[3] Gingras et al., Physical Review Letters 123, 217005 (2019).

[4] Gingras et al., Physical Review B 106, 064513 (2022).