Topological Insulator in Twisted Transition Metal Dichalcogenide Heterotrilayers

TL;DR

This paper demonstrates that twisted trilayer transition metal dichalcogenides can host topological insulator phases due to moiré potential symmetries, revealing new topological states in multilayer moiré superlattices.

Contribution

It introduces the concept of topological phases in twisted TMD heterotrilayers with $C_6$ symmetry, expanding the understanding of topological states in multilayer moiré systems.

Findings

Twisted trilayer TMDs can become topological insulators under certain moiré potentials.

Edge states are confirmed via local density calculations at topological minigaps.

Mosaic patterns of topological and trivial insulators emerge in specific heterostructures.

Abstract

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\'e superlattices remain to be further explored. In twisted TMDs heterotrilayers, the realization of moir\'e potential with various symmetries becomes feasible. Here, we demonstrate that twisted trilayer TMDs can enter a topological insulator phase under the influence of moir\'e 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 moir\'e WS$_2$/WSe$_2$/MoS$_2$ heterotrilayers where only the middle layer is twisted, the maxima of the moir\'e 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 moir\'e edge states. In the helical twisted AA-stacked moir\'e 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 moir\'e potential possessing $C_6$ symmetry. The results provide a new way for the experimental realization of topological phases in TMDs heterojunctions.