Reentrant topological phase in half-Heusler compounds

Half-Heusler compounds are known for their various compositions and multifunctional properties including topological phases. In this study, we investigate the topological classification of this class of materials based on the ordering of the $\Gamma_6$, $\Gamma_8$ states, and a previously overlooked $\Gamma_6^*$ state, during an adiabatic expansion process. Using first-principles calculations based on density functional theory, we observed that the non-trivial topology is governed by a three-band mechanism. We provide a simple model derived from $k\cdot p$ Hamiltonian that interprets the topological phase in half-Heusler systems. Additionally, we explore the robustness of the topological phase under tension and a new perspective on the topological nature of half-Heusler compounds.