Phase transitions in transition-metal dichalcogenides with strain: Insights from first-principles calculations

It is well known that monolayer transition-metal dichalcogenides (MX$_2$, M = Mo, W and X = S, Se, Te) could exist in three common structures, i.e. 1$T$, 1$T'$, and 1$H$ phases. In order to reveal their possible phase transitions driven by biaxial strain, we use first-principles calculations to determine the energy landscapes associated with these three phases. Due to its intrinsic dynamical instability, the centrosymmetric 1$T$ phase is known to be metastable and will transform into the 1$T'$ phase where pairs of metal atoms pull together toward each other. Moreover, controlling the metallic 1$T'$ and semiconducting 1$H$ phases is of particular interest as this can introduce novel opportunities in a series of applications. When a biaxial strain is simultaneously compressed along the zigzag direction and stretched along the armchair direction，phase transitions from 1$H$ to 1$T'$ have occurred in MSe$_2$ and MoTe$_2$, but for MSe$_2$ the biaxial strain is much difficult to realize in experiments. For WTe$_2$, the 1$T'$ structure will transform into the 1$H$ form when a biaxial strain is just compressed along the armchair direction. The transitions between 1$H$ and 1$T'$ phases could be attributed to the changes of metal-chalcogen bonds along the armchair direction by analyzing the Crystal Orbital Hamilton Population. Only half M-X bonds along the armchair direction is the main factor, because their lengths are robust in 1$T'$ phase and decrease in 1$H$ form with the tensile strain applied along the armchair direction. Our findings provide a guideline for the phase engineering of transition-metal dichalcogenides with biaxial strain.