Singlet-Quintet Mixing in Spin-Orbit Coupled Superconductors with j=3/2 Fermions

In non-centrosymmetric superconductors, spin-orbit coupling can induce an unconventional superconducting state with a mixture of s-wave spin-singlet and p-wave spin-triplet channels, which leads to a variety of exotic phenomena, including anisotropic upper critical field, magnetoelectric effect, topological superconductivity, et al. It is commonly thought that inversion symmetry breaking is substantial for pairing-mixed superconducting states. In this work, we theoretically propose that a new type of pairing-mixed state, namely the mixture of s-wave spin-singlet and d-wave spin-quintet channels, can be induced by spin-orbit coupling even in the presence of inversion symmetry when electrons effectively carry "spin-3/2" in superconductors. As a physical consequence of the singlet-quintet pairing mixing, topological nodal-line superconductivity is found in such system and gives rise to flat surface Majorana bands. Our work provides a possible explanation of unconventional superconducting behaviors observed in superconducting half-Heusler compounds.