Hund's coupling stabilized superconductivity in the presence of spin-orbit interactions

TL;DR

This paper demonstrates that Hund's coupling can stabilize superconductivity with spin-triplet, orbital-singlet pairing in systems with spin-orbit interactions, especially in tetragonal and octahedral multi-orbital systems.

Contribution

It reveals how Hund's interactions and spin-orbit coupling together influence the nature of superconducting pairing in multi-orbital systems with different symmetries.

Findings

Spin-orbit interactions can stabilize spin-triplet, orbital-singlet pairing channels.

Superconducting pairing depends critically on the number of bands crossing the Fermi level.

Hund's coupling enhances the stability of unconventional pairing states.

Abstract

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 $U^\prime$ and Hund's 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 spin triplet, orbital singlet character. Depending on the form of spin-orbit coupling, pairing channels belonging to degenerate, non-trivial 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.