Strontium Ruthenate's Superconducting Symmetries from First-Principles Calculations*

The normal state of Sr₂RuO₄ is well understood but its superconducting state is still a subject of major debates [1]. From a first-principles correlated multiorbital calculation, we construct the spin and charge fluctuation pairing interactions. These interactions depend on the proximity to an instability and on the size of the screened Hund's coupling. We present the leading gap function symmetries obtained by solving the frequency-dependent linearized Eliashberg equation for the case where spin-orbit coupling is neglected [2]. Close to magnetic instabilities, we find spin-singlet d-wave pairing. Away, where charge fluctuations increase, we observe the emergence of two even-parity spin-triplet states: an odd in frequency s wave and two degenerate momentum-independent states that pair electrons on different orbitals and are odd in orbital indices. These exotic states are compared with experiments. Moreover, we discuss and present the effects of spin-orbit coupling and uniaxial strain on the system.

[1] Pustogow et al., Nature 574, 72 (2019)
[2] Gingras et al., arXiv:1808.02527, accepted in Phys. Rev. Lett. (2019)