First-principles calculations have been performed to study the evolution of the inverted bands and the topological phase diagrams of monoclinic transition-metal dichalcogenide monolayers ($1T^{\prime }\text{−}M{X}_2$ with $M=\text{Mo}$, W and $X=\text{S}$, Se, Te) under strain. We find that the band topology undergoes a nontrivial to trivial transition in compressed systems due to the strain-sensitive inverted $p$-orbital and $d$-orbital bands, which exhibit an anisotropic evolution behavior with respect to the strain orientation. In $M{\mathrm{Te}}_2$, the normally ordered $p_y$ and $d$ bands at the $X$ point are inverted mainly by compressive strain along the $y$ direction (${\epsilon }_y$), which, together with the unchanged inverted bands at the $\mathrm{\Gamma }$ point, turns the topology trivial. In $M{\mathrm{S}}_2$ and $M{\mathrm{Se}}_2$, the inverted $p_x$ and $d$ bands at $\mathrm{\Gamma }$ become normally ordered under a large compressive strain along the $x$ direction (${\epsilon }_x$). $M{\mathrm{Te}}_2$ acquires a much smaller critical strain for the topological phase transition (TPT) than S- and Se-based systems due to strain-sensitive head-to-head bonding between the $p_y$ orbitals. Particularly, the critical compressive ${\epsilon }_y$ can be further reduced by applying tensile ${\epsilon }_x$ for $M{\mathrm{Te}}_2$. Our results provide a concrete mechanism behind the nontrivial band topology in $1T^{\prime }\text{−}M{X}_2$ and a guide for applying strain to control the TPT.

• Received 26 April 2017

DOI:https://doi.org/10.1103/PhysRevB.95.245436