Understanding topological phase transition in monolayer transition metal dichalcogenides

Despite considerable interest in layered transition metal dichalcogenides (TMDs), such as $M{X}_2$ with $M=(\mathrm{Mo},\mathrm{W})$ and $X=(\mathrm{S},\mathrm{Se},\mathrm{Te})$, the physical origin of their topological nature is still poorly understood. In the conventional view of topological phase transition (TPT), the nontrivial topology of electron bands in TMDs is caused by the band inversion between metal $d$- and chalcogen $p$-orbital bands where the former is pulled down below the latter. Here, we show that, in TMDs, the TPT is entirely different from the conventional speculation. In particular, $M{\mathrm{S}}_2$ and $M\mathrm{S}{\mathrm{e}}_2$ exhibits the opposite behavior of TPT such that the chalcogen $p$-orbital band moves down below the metal $d$-orbital band. More interestingly, in $M\mathrm{T}{\mathrm{e}}_2$, the band inversion occurs between the metal $d$-orbital bands. Our findings cast doubts on the common view of TPT and provide clear guidelines for understanding the topological nature in new topological materials to be discovered.