Topological states on grain boundary of 1T’-MoTe₂

We show that on a transition metal dichalcogenides 1T’ MoTe₂ two types of grain boundaries can exist and that electronic states associated with themselves strongly depend on their crystal symmetries as well as topological index. Using first-principles computational methods and model Hamiltonian analysis, we investigate their structural stabilities and electronic structures. We clearly demonstrate that one-dimensional metallic state along one of the grain boundaries is a topologically protected state. The spatial symmetries created by grain boundaries is also shown to play an important role in characterizing the protected metallic states.