  YPtBi, a topological semimetal with very low carrier density, was recently
found to be superconducting below $T_\mathrm{c} = 0.77$\,K. In the 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 the
Half-Heusler structure.
