Topological invariant and domain connectivity in moiré materials

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 that 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 of the truncation condition, which is specific to moiré materials. We demonstrate these correspondences in the twisted Bernevig-Hughes-Zhang model by tuning its moiré periodic mass term. 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.