Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors

Nonunitary superconductivity has attracted renewed interest as a novel gapless phase of matter. In this study, we investigate the superconducting gap structure of nonunitary odd-parity chiral pairing states in a superconductor involving strong spin-orbit interactions. By applying a group theoretical classification of chiral states in terms of discrete rotation symmetry, we categorized all possible point-nodal gap structures in nonunitary chiral states into four types in terms of the topological number of nodes and node positions relative to the rotation axis. In addition to conventional Dirac and Weyl point nodes, we identify a type of Dirac point nodes unique to nonunitary chiral superconducting states. Such a Dirac point node is a nodal point of two pseudospin excitations, but the dispersions around it depend on the pseudospin. The node type can be identified experimentally based on the temperature dependence of the nuclear magnetic resonance longitudinal relaxation rate. The implication of our results for a nonunitary odd-parity superconductor in UTe2 is also discussed.