Topological phase transition in the ternary half-Heusler alloy ZrIrBi

Half-Heusler alloys provide a new platform for deriving a host of topologically exotic compounds through the inherent flexibility of tuning their hybridization strength (via lattice parameters), spin-orbit strength, substitution/doping, etc. Using the first-principles calculation within the density functional theory, we explore the possibility of realizing a topological insulating phase in a new half-Heusler material ZrIrBi. We discovered three routes through which ZrIrBi can be transformed to exhibit a topological nontrivial phase. They are (i) a hydrostatic expansion by 1% causing a band inversion with zero gap, (ii) a uniaxial strain along (001) direction which opens a band gap while preserving the inverted band order, and (iii) substitution of 50% Bi by As and 50% Zr by Hf forming the compounds $\mathrm{ZrIr}({\mathrm{As}}_0.5{\mathrm{Bi}}_0.5$) and $({\mathrm{Zr}}_0.5{\mathrm{Hf}}_0.5$)IrBi again showing a topologically nontrivial band inversion. A definitive proof of the surface conduction in all three cases are done by simulating surface band structures. We report the formation energies and the phonon dispersion for the three cases to confirm the chemical and mechanical stability of the compounds.