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In non-centrosymmetric superconductors, spin-orbit coupling can induce anunconventional superconducting state with a mixture of s-wave spin-singlet andp-wave spin-triplet channels, which leads to a variety of exotic phenomena,including anisotropic upper critical field, magnetoelectric effect, topologicalsuperconductivity, et al. It is commonly thought that inversion symmetrybreaking is substantial for pairing-mixed superconducting states. In this work,we theoretically propose that a new type of pairing-mixed state, namely themixture of s-wave spin-singlet and d-wave spin-quintet channels, can be inducedby spin-orbit coupling even in the presence of inversion symmetry whenelectrons effectively carry "spin-3/2" in superconductors. As a physicalconsequence of the singlet-quintet pairing mixing, topological nodal-linesuperconductivity is found in such system and gives rise to flat surfaceMajorana bands. Our work provides a possible explanation of unconventionalsuperconducting behaviors observed in superconducting half-Heusler compounds.

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