Metallic surface electronic state in half-Heusler compounds RPtBi (R= Lu, Dy, Gd)

Rare-earth platinum bismuth ($R$PtBi) has been proposed recently as a potential topological insulator. In this paper, we present measurements of the metallic surface electronic structure in three members of this family, using angle-resolved photoemission spectroscopy (ARPES). Our data show clear spin-orbit splitting of the surface bands and the Kramers' degeneracy of spins at the $\mathrm{\ensuremath{\Gamma}\ifmmode \bar{}\else \={}\fi{}}$ and $\mathrm{M\ifmmode \bar{}\else \={}\fi{}}$ points, which is reproduced nicely with our full-potential linearized augmented plane wave calculation for a surface electronic state. Topologically nontrivial behavior is signified by band inversion in the calculated bulk electronic structures, yet no direct indication of such behavior is detected by ARPES except for a weak Fermi crossing detected in close proximity to the $\mathrm{\ensuremath{\Gamma}\ifmmode \bar{}\else \={}\fi{}}$ point, making the total number of Fermi crossings odd. In the surface band calculation, however, this crossing is explained by a Kramers pair of bands that are very close to each other. The classification of this family of materials as topological insulators remains an open question.