Superconductivity in the presence of spin-orbit interactions stabilized by Hund coupling

The intraorbital repulsive Hubbard interaction cannot lead to attractive superconducting pairing states, except through the Kohn-Luttinger mechanism. This situation may change when we include additional local interactions such as the interorbital repulsion ${U}^{\ensuremath{'}}$ and Hund interactions $J$. Adding these local interactions, we study the nature of the superconducting pairs in systems with tetragonal crystal symmetry including the ${d}_{xz}$ and ${d}_{yz}$ orbitals, and in octahedral systems including all three of ${d}_{xz}, {d}_{yz}$, and ${d}_{xy}$ orbitals. In the tetragonal case, spin-orbit interactions can stabilize attractive pairing channels containing a spin triplet, orbital singlet character. Depending on the form of spin-orbit coupling, pairing channels belonging to degenerate, nontrivial irreducible representations may be stabilized. In the octahedral case, the pairing interactions of superconducting channels are found to depend critically on the number of bands crossing the Fermi energy.