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Half-Heusler systems host a plethora of different ground states, especiallywith non-trivial topology. However, there is still a lack of spectroscopicinsight into the corresponding band inversion in this family. In this work, welocally explore the half-Heuslers Y$T$Bi ($T =$ Pt and Pd) by means of scanningtunneling microscopy/spectroscopy. From our analysis of the (120) surfaceplane, we infer that the increase of the spin--orbit coupling upon going fromPd to Pt is the main player in tuning the surface states from trivial totopologically non-trivial. Our measurements unveil a ($2 \times 1$)reconstruction of the (120) surface of both systems. Using density functionaltheory calculations, we show that the observed different behavior of the localdensity of states near the Fermi level in these two materials is directlyrelated to the presence of metallic surface states. Our work sheds new light ona well known tunable family of materials and opens new routes to explore thepresence of topological states of matter in half-Heusler systems and itsmicroscopic observation.

Tuning the topological character of half-Heusler systems: A comparative study on Y$T$Bi ($T$ = Pd, Pt)