Effects of longer-range interaction on superconductivity in Sr₂RuO₄

The symmetry of the superconducting order parameter (OP) in Sr₂RuO₄ remains a puzzle. None of the currently proposed OPs can account for all important experiments, highlighting the importance of exploring different alternatives. Recently, d_x²-y² + ig_xy(x²-y²) and d_x²-y² + i(p_x ± p_y) have been proposed as OP candidates. The g_xy(x²-y²) -wave component has not been found to be stable in on-site multi-orbital Hubbard interaction. In this work, we investigate the effect of longer-range interactions on different Cooper pairing channels in different regimes of the interaction parameter space. Our study combines a weak-coupling renormalization group and random phase approximation calculations. From the OPs found in the dominant pairing channels, we further study experimental implications, such as spontaneous edge currents due to possible spontaneous time-reversal symmetry breaking when two OPs are degenerate or are close to degeneracy.