Nontrivial Topological Phases in Ternary Borides M₂XB₂ (M=W, Mo; X=Co, Ni)

The nontrivial band topologies protected by certain symmetries have attracted significant interest in condensed matter physics. The discoveries of nontrivial topological phases in real materials provide a series of archetype materials to further explore the topological physics. Ternary borides M₂XB₂ (M = W, Mo; X = Co, Ni) have been widely investigated as the wear-resistant and high-hardness materials. Based on first-principles calculations, we find the nontrivial topological properties in these materials. Taking W₂NiB₂ as an example, this material shows the nodal line semimetal state in the absence of spin-orbit coupling. Two types of nodal lines appear near the Fermi level simultaneously. One is protected by the combined space-inversion and time-reversal symmetry, and the other is by the mirror symmetry. Part of these two-type nodal lines form nodal chains. When spin-orbit coupling is included, these nodal lines are fully gapped and the system becomes a strong topological insulator with nontrivial Z₂ index (1;000). Our calculations demonstrate that a nontrivial spin-momentum locked surface Dirac cone appears on the $(\overline{1}10)$ surface. We also find that other isostructural ternary borides Mo₂NiB₂, Mo₂CoB₂, and W₂CoB₂ possess similar topological band structures. Therefore, our work not only enriches the understanding of band topology for ternary borides, but also lays the foundation for the further study of topological phases manipulation and potential spintronic applications in realistic materials.