Spin-orbit coupling effects on Hund's coupling induced orbital-singlet spin-triplet superconductivity

We study the effect of spin-orbit coupling (SOC) on the Hund's coupling induced orbital-singlet spin-triplet superconductivity in the three-orbital Hubbard model with rotationally-invariant slave-boson (RISB) mean-field theory. In the absence of SOC, RISB reproduces the phase diagram similar to the one obtained from dynamical mean-field theory, where the superconducting state emerges from the Hund's metal crossover regime. In the presence of SOC, the intrinsic particle-hole asymmetry in atomic levels, introduced by SOC, leads to different superconducting behaviors for above and below half-filling; the SOC suppresses the superconductivity in these two regimes with distinct manners. We analyze how these behaviors are connected to the spin and charge fluctuations and the atomic multiplets statistics. Our results provide insight into the pairing mechanism in Sr₂RuO₄ and iron-based superconductors.