Abstract
Recently, a moiré material has been proposed in which multiple domains of different topological phases appear in the moiré unit cell due to a large moiré modulation. Topological properties of such moiré materials may differ from those of the original untwisted layered material. In this paper, we study how the topological properties are determined in moiré materials with multiple topological domains. We show a correspondence between the topological invariant of moiré materials at the Fermi level and the topology of the domain structure in real space. We also find a bulk-edge correspondence that is compatible with a continuous change in the truncation condition, which is specific to moiré materials. We demonstrate these correspondences in the twisted Bernevig-Hughes-Zhang model that describes general -indicated topological insulator phases, by tuning its domain structure in the moiré unit cell. The obtained result can only be used to determine the topology at the Fermi level in the charge-neutral condition, but it can be combined with the traditional Wilson loop analysis to determine topologies of other gaps around. These results give a feasible method to evaluate a topological invariant for all occupied bands of a moiré material and contribute to the design of topological moiré materials and devices.
5 More- Received 21 December 2022
- Revised 8 March 2023
- Accepted 15 March 2023
DOI:https://doi.org/10.1103/PhysRevB.107.125308
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