Topological Insulator in Twisted Transition Metal Dichalcogenide Heterotrilayers

The quantum spin Hall effect has been predicted in twisted homobilayer transition metal dichalcogenides (TMDs) owing to the layer-pseudospin magnetic field. Recently, experimental observations have also confirmed such topological states of matter. However, the topological electronic properties in multilayer moiré superlattices remain to be further explored. In twisted TMDs heterotrilayers, the realization of moiré potential with various symmetries becomes feasible. Here, we demonstrate that twisted trilayer TMDs can enter a topological insulator phase under the influence of moiré potential with ${C_6}$ symmetry. Specifically, we built two types of trilayer heterostructures, where the low-energy valence band electrons are contributed by the middle layer. In the AA-stacked moiré WS$_2$/WSe$_2$/MoS$_2$ heterotrilayers where only the middle layer is twisted, the maxima of the moiré potential exhibits an approximate ${C_6}$ symmetry. The $C_6$ symmetry effectively compensates for the spatial inversion symmetry breaking in the WSe$_2$ layer, leading to a twist-angle-dependent topological phase transition. Leveraging a Green's function approach, we calculate the local state density of edge states at topological minigaps, confirming their nature as moiré edge states. In the helical twisted AA-stacked moiré MoS$_2$/WSe$_2$/MoS$_2$ heterotrilayers, we observed a mosaic pattern of topological and trivial insulators. The emergence of topological mosaic is attributed to the maxima of the local moiré potential possessing $C_6$ symmetry. The results provide a new way for the experimental realization of topological phases in TMDs heterojunctions.