Topological electronic structure in half-Heusler topological insulators

Abstract

We have investigated band structures of a series of 28 ternary half-Heusler compounds $M{M}^{\ensuremath{'}}X$ of MgAgAs type, where $M=(\text{Lu},\text{La},\text{Sc},\text{Y})$ and ${M}^{\ensuremath{'}}X=(\text{PtBi},\text{AuPb},\text{PdBi},\text{PtSb},\text{AuSn},\text{NiBi},\text{PdSb})$. Our results show that the ${Z}_{2}$ topological order is due to a single band inversion at the $\ensuremath{\Gamma}$ 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 ${Z}_{2}$ topological insulators in nonmagnetic ternary compounds.