Topological invariant and domain connectivity in moir\'e materials

TL;DR

This paper explores how topological invariants in moiré materials relate to their domain structures, revealing a bulk-edge correspondence and providing a method to evaluate topological properties in these complex systems.

Contribution

It establishes a correspondence between topological invariants and domain topology in moiré materials, introducing a method to evaluate topological properties across all occupied bands.

Findings

Topological invariants are linked to domain structures in moiré materials.

A bulk-edge correspondence is demonstrated for moiré systems.

The method is validated using the twisted BHZ model.

Abstract

Recently, a moir\'e material has been proposed in which multiple domains of different topological phases appear in the moir\'e unit cell due to a large moir\'e modulation. Topological properties of such moir\'e materials may differ from that of the original untwisted layered material. In this paper, we study how the topological properties are determined in moir\'e materials with multiple topological domains. We show a correspondence between the topological invariant of moir\'e 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 moir\'e materials. We demonstrate these correspondences in the twisted Bernevig-Hughes-Zhang model by tuning its moir\'e periodic mass term. These results give a feasible method to evaluate a topological invariant for all occupied bands of a moir\'e material, and contribute to the design of topological moir\'e materials and devices.