Unconventional Superconductivity in YPtBi and Related Topological Semimetals.

YPtBi, a topological semimetal with a very low carrier density, was recently found to be superconducting below T_{c}=0.77  K. In conventional theory, the nearly vanishing density of states around the Fermi level would imply a vanishing electron-phonon coupling and would, therefore, not allow for superconductivity. Based on relativistic density-functional theory calculations of the electron-phonon coupling in YPtBi, it is found that carrier concentrations of more than 10^{21}  cm^{-3} are required to explain the observed critical temperature with the conventional pairing mechanism, which is several orders of magnitude larger than experimentally observed. It is very likely that an unconventional pairing mechanism is responsible for the superconductivity in YPtBi and related topological semimetals with half-Heusler structure.