Topological invariant and domain connectivity in moiré materials

Moiré materials have become one of the most active fields in material science in recent years due to their high tunability and wide variety of quantum phases. Very recently, a moiré material in which topological insulator domains and normal insulator domains coexist in the moiré unit cell has been proposed. In this presentation, we show a correspondence between the topology of the domain structure in real space and a topological invariant of the moiré material at the charge neutral point. We also found a bulk-edge corresponding that is compatible with a continuous change of the truncation condition, which is specific in moiré materials. We demonstrate the correspondence in twisted Bernevig-Hughes-Zhang model by tuning its moiré periodic mass term. This result is expected to contribute to the design of moiré materials with more diverse quantum properties.