Topological phase transition in half-Heusler compounds HfIrX (X = As, Sb, Bi)

• We find topological insulator and Weyl-semimetal in HfIrX (X = As, Sb, Bi).
• We control the topological phases transition by the pressure and atoms substitution.
• We explained the physical reasons of the topological phases transition.

We studied the lattice constant and atoms substitution tunable topological phase transition in the half-Heusler compounds HfIrX (X = As, Sb, Bi). At the equilibrium cubic crystal structure and excluding SOC, HfIrAs and HfIrBi are topological nontrivial semimetal, while HfIrSb is a trivial topological insulator. This is because that the “internal pressure” lifts the s-type Γ1Γ1 band above p-type Γ5Γ5 bands in HfIrSb. When SOC is included, HfIrAs and HfIrSb become topological insulator, and normal band insulator, respectively, while HfIrBi is still a topological semimetal. When we induce compressive stress in the ab-plane of HfIrBi, it becomes a Weyl semimetal, with eight Weyl-Points (WPS) at (±±Kx, 0, ±±Kz), (0, ±Ky,±±Ky,±Kz), Kx = Ky = 0.023 Å−1, Kz = 0.108 Å−1.

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