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 moir & eacute; superlattices remain to be further explored. In twisted TMDs heterotrilayers, the realization of a moir & eacute; potential with various symmetries becomes feasible. Here, we demonstrate that twisted trilayer TMDs can enter a topological insulator phase under the influence of a moir & eacute; potential with C6 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 moir & eacute; WS2/WSe2/MoS2 heterotrilayers where only the middle layer is twisted, the maxima of the moir & eacute; potential exhibit an approximate C6 symmetry. The C6 symmetry effectively compensates for the spatial inversion symmetry breaking in the WSe2 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 moir & eacute; edge states. In the helical twisted AA-stacked moir & eacute; MoS2/WSe2/MoS2 heterotrilayers, we observed a mosaic pattern of topological and trivial insulators. The emergence of a topological mosaic is attributed to the maxima of the local moir & eacute; potential possessing C6 symmetry. The results provide a way for the experimental realization of topological phases in TMDs heterojunctions.