Spin-orbit coupled superconductivity with spin-singlet nonunitary pairing

The gap functions for a single-band model for unconventional superconductivity are distinguished by their unitary or nonunitary forms. Here we generalize this classification to a two-band superconductor with two nearly degenerate orbitals. We focus on spin-singlet pairings and investigate the effects of the atomic spin-orbit coupling (SOC) on superconductivity, which is a driving force behind the discovery of a new spin-orbit coupled nonunitary superconductor. Multiorbital effects such as orbital hybridization and strain-induced anisotropy will also be considered. The spin-orbit coupled nonunitary superconductor has three main features. First, the atomic SOC locks the electron spins to be out-of-plane, leading to a new Type II Ising superconductor with a large in-plane upper critical field beyond the conventional Pauli limit. Second, it provides a promising platform to realize the topological chiral or helical Majorana edge state even without external magnetic fields or Zeeman fields. More surprisingly, a spin-polarized superconducting state could be generated by spin-singlet nonunitary pairings when time-reversal symmetry is spontaneously broken, which serves as a smoking gun to detect this exotic state by measuring the spin-resolved density of states. Our work indicates the essential roles of orbital-triplet pairings in both unconventional and topological superconductivity.