Effects of dynamic local correlation on the spin susceptibility and superconducting symmetries in Sr₂RuO₄

Sr₂RuO₄ remains as one of most intriguing superconductors with the possibility of highly exotic and unconventional superconductivity, often regarded having p_x+ip_y order parameter with spin-triplet and chiral electron pairing. In the normal state, it is classified as a Hund’s metal where Hund’s coupling plays a central role in the local electronic correlation.

Here we demonstrate how the dynamic local correlations shape the susceptibility in the k-space and the pairing symmetry within the framework of density-functional theory combined with dynamical mean-field theory (DFT+DMFT). We find that using frequency-dependent two-particle vertex moves the zero energy spin susceptibility peaks towards the Gamma point, compared with random-phase approximation which basically retains the peak positions closer to the Brillouin zone boundary as determined by the Fermi-surface nesting. d_xy orbital plays a central role here via its enhanced correlation strength. When linearized-Eliashberg equation is constructed from the susceptibility and solved, the prime candidate of the superconducting gap symmetry is a nodal s-wave, as well as a nearly degenerate d-wave solution, all in spin singlet. Furthermore, another set of degenerate spin singlet gap functions emerges, odd with respect to both k-point and orbital exchanges. We discuss the compatibility of these gap functions with experimental observations.