Multi-Orbital B_1g Superconducting Order Parameter with Complex Components Induced by Spin-Orbit Coupling in Strontium Ruthenate

Strontium ruthenate is an archetypal unconventional superconductor yet experiments give seemingly different pictures for the symmetry of its superconducting order parameter. Starting from a realistic electronic structure, we solve the frequency dependent Eliashberg equations with a spin-fluctuation pairing vertex. Varying interaction strength and Hund's coupling, we found a phase diagram with three candidate order parameters when spin-orbit coupling is neglected: 1) a spin-singlet d-wave, 2) a momentum-independent inter-orbital spin-triplet and 3) a spin-triplet odd-frequency s-wave [1]. Including spin-orbit coupling, we find that 1) and 2) are both parts of a same multi-orbital order parameter which transforms like the one-component B_1g irreducible representation. We show that this order parameter has to be complex and find that it includes odd-frequency contributions that make it appear to break time-reversal symmetry. Comparison with experiments will be presented.

[1] Gingras et al., Phys. Rev. Lett. 123, 217005 (2019).