Singlet-quintet mixing in spin-orbit coupled superconductors with j= 32 fermions

In noncentrosymmetric superconductors, spin-orbit coupling can induce an unconventional superconducting state with a mixture of s-wave spin-singlet and p-wave spin-triplet channels. It is commonly thought that inversion symmetry breaking is substantial for mixed-pairing superconducting states. In this paper, we theoretically propose that a new type of mixed-pairing state, namely the mixture of s-wave spin-singlet and d-wave spin-quintet channels, can occur even in the presence of inversion symmetry when electrons effectively carry "spin-3/2." As a physical consequence of the singlet-quintet pairing mixing, topological nodal-line superconductivity is found in such a 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 and suggests that these superconducting materials provide a new platform for exploring unconventional and topological superconductivity.