Multi-component electronic systems are not rare in solid state physics due to the multi-orbital band structure and spin-orbit coupling. They exhibit richer structures of topological superconductivity beyond the conventional scenarios of spin singlet and triplet pairings. We generalize the He3-B type isotropic p-wave topological pairing to the four-component fermion systems, which are effectively described by spin-3/2 fermions. The p-wave triplet and f-wave septet pairings are identified as topologically non-trivial characterized by large topological indices and exhibiting high order Majorana-Dirac surface spectra. Recently, there has been experimental evidence of nodal spin-3/2 superconductivity in the half-Heusler compound YPtBi semi-metal with theoretically proposed p-wave septet pairing gap function. Zero energy Majorana flat bands on the (111)-surface and their signatures in the quasi-particle interference patterns are calculated. In addition, we also discuss how to realize the chiral Majorana modes by a “boundary of boundary” method starting with a degenerate Fermi surface without spin-orbit coupling. The superconductors develop spontaneous magnetizations on the surfaces. Along the magnetic domain walls on the surface, the chiral Majorana modes propagate unidirectionally, which can be controlled by external magnetic fields.

References: 

[1] Wang Yang, Yi Li, Congjun Wu, ``Topological septet pairing with spin-3/2 fermions -- high partial-wave channel counterpart of the He3-B phase", Phys. Rev. Lett. 117, 075301 (2016).

[2] Wang Yang, Tao Xiang, and Congjun Wu, ``Majorana surface modes and nodal topological pairings in spin-3/2 semimetals", Phys. Rev. B 94, 144154 (2017).

[3] Wang Yang, Chao Xu, and Congjun Wu, ``Spontaneous surface magnetization and chiral Majorana modes in the $p\pm is$ superconductors", arxiv:1711.05241.