Engineering Miniband Topology via Band-Folding in Moir\'e Superlattice Materials

TL;DR

This paper introduces a band-folding mechanism induced by moiré superlattice potentials to engineer topological minibands in moiré materials, enabling the design of non-trivial topological phases with potential experimental applications.

Contribution

It proposes a novel band-inversion mechanism via band-folding in moiré superlattices and develops a general theoretical framework for topological miniband engineering.

Findings

Moiré minibands with non-trivial topology identified

Topological phase diagrams constructed for moiré models

General band representation theory developed for moiré systems

Abstract

The emergence of topologically non-trivial flat bands in moir\'e materials provides an opportunity to explore the interplay between topological physics and correlation effects, leading to the recent experimental realization of interacting topological phases, e.g. fractional Chern insulators. In this work, we propose a mechanism of band inversion induced by band-folding from the moir\'e superlattice potential for engineering topological minibands in moir\'e materials. We illustrate this mechanism via two classes of model Hamiltonians, namely the Rashba model and the Bernevig-Hughes-Zhang (BHZ) model, under the moir\'e superlattice potentials. Moir\'e minibands with non-trivial band topology, including Z2 number, mirror Chern number and fragile topology, have been found and the topological phase diagram is constructed for these moir\'e models. A general theory based on band representations in the mori\'e Brillouin zone is also developed for a generalization of this mechanism to other space groups. Possible experimental realizations of our model Hamiltonian are discussed.