Lattice Model For The Quantum Anomalous Hall Effect in Moir\'e Graphene

Abstract

Inspired by experiments on magic angle twisted bilayer graphene, we present a lattice mean-field model for the quantum anomalous Hall effect in a moir\'e setting. Our hopping model thus provides a simple route to a moir\'e Chern insulator in commensurately twisted models. We present a study of our model in the ribbon geometry, in which we demonstrate the presence of thick chiral edge states that have a transverse localization that scales with the moir\'e lattice spacing. We also study the electronic structure of a domain wall between opposite Chern insulators. Our model and results are relevant to experiments that will image or manipulate the moir\'e quantum anomalous Hall edge states.