Topological electronic structure in half-Heusler topological insulators

We have investigated band structures of a series of 28 ternary half-Heusler compounds M M′ X of MgAgAs type, where M= (Lu,La,Sc,Y) and M′ X= (PtBi,AuPb,PdBi,PtSb,AuSn,NiBi,PdSb). Our results show that the Z₂ topological order is due to a single band inversion at the Γ point. In native states, these half-Heusler compounds are identified as being topologically nontrivial semimetals, or nontrivial metals, or trivial insulators, which can be turned into insulating thin films on suitable substrates. Our analysis reveals a straightforward relationship which connects the band inversion strength (extent of deviation from the critical point) to the atomic charge of constituents and the lattice parameter. Our findings suggest a general method for identifying Z₂ topological insulators in nonmagnetic ternary compounds.