Chiral surface superconductivity in half-Heusler semimetals

We propose the metallic and weakly dispersive surface states of half Heusler semimetals as a possible domain for unconventional superconductivity. Using density functional theory (DFT) calculations and the random phase approximation (RPA), we analyse the surface band structure of LuPtBi and its propensity towards Cooper pair formation induced by screened electron-electron interactions. Pair wave functions transforming under the two-fold degenerate E irreducible representation of the surface's $C_{3v}$ point group are found to be favoured by unconventional mechanisms over a wide range of parameters. We show that this naturally results in a chiral superconducting condensate that spontaneously breaks time-reversal symmetry and features pairs of dispersing Majorana edge modes.