Hund's Coupling Stabilized Superconductivity in the Presence of Spin Orbit Interactions

Local repulsive Coulomb interactions cannot lead to attractive superconducting pairing states, except through the Kohn-Luttinger mechanism. The situation may change however when we include additional local interactions such as the interorbital repulsion $U^\prime$ and Hund's interactions $J$. Including these local interactions, we study the nature of the superconducting pairs in a system including the $d_{xz},d_{yz}$, and $d_{xy}$ orbitals within octahedral and tetragonal crystal environments. It is found that in the presence of spin orbit interactions, attractive pairing states can be stabilized that contain spin triplet, orbital singlet character. The energy and structure of these states change as the degree of tetragonal distortion is tuned away from the cubic limit. Our results extend the work of earlier studies which were restricted to two orbital systems in two dimensions and support the notion that local atomic interactions, in tandem with spin orbit interactions, can lead to novel spin triplet superconducting states.