Majorana surface modes of topological septet pairing in spin-$3/2$ semi-metals

Multi-component electronic systems exhibit richer structures of topological superconductivity beyond the conventional scenarios of spin singlet and triplet pairings in spin-$1/2$ systems. Examples include the half-Heusler compounds RPtBi series (R for rare earth), whose electronic structures are described by effective spin-$3/2$ particles due to strong spin-orbit coupling. Recent experiments provide evidence to unconventional superconductivity in these materials with nodal spin septet pairing. We systematically study topological pairing structures in spin-$3/2$ systems and calculate surface spectrum, which exhibit zero energy flat band and cubic dispersion. These unusual features of surface states can be tested in future spectroscopy experiments.