Quantum anomalous Hall crystals in moir\'e bands with higher Chern number

TL;DR

This paper demonstrates the existence and stability of quantum anomalous Hall crystals with higher Chern number in moiré materials, specifically twisted multilayer graphene, providing experimental guidance and expanding topological phase understanding.

Contribution

It introduces stable QAHCs with C=2 in moiré bands at fractional filling, supported by exact diagonalization, and offers practical parameters for experimental realization.

Findings

QAHCs with C=2 are stable at 2/3 filling in moiré bands.

Robustness of QAHC in twisted bilayer-trilayer graphene.

Guidelines for experimental tuning of twist angle and electric field.

Abstract

The realization of fractional Chern insulators in moir\'e materials has sparked the search for further novel phases of matter in this platform. In particular, recent works have demonstrated the possibility of realizing quantum anomalous Hall crystals (QAHCs), which combine the zero-field quantum Hall effect with spontaneously broken discrete translation symmetry. Here, we employ exact diagonalization to demonstrate the existence of stable QAHCs arising from $\frac{2}{3}$-filled moir\'e bands with Chern number $C=2$. Our calculations show that these topological crystals, which are characterized by a quantized Hall conductivity of $1$ (in units of $e^2/h$) and a tripled unit cell, are robust in an ideal model of twisted bilayer-trilayer graphene -- providing a novel explanation for experimental observations in this heterostructure. Furthermore, we predict that the QAHC remains robust in a realistic model of twisted double bilayer graphene and, in addition, we provide a range of optimal tuning parameters, namely twist angle and electric field, for experimentally realizing this phase. Overall, our work demonstrates the stability of QAHCs at odd-denominator filling of $C=2$ bands, provides specific guidelines for future experiments, and establishes chiral multilayer graphene as a theoretical platform for studying topological phases beyond the Landau-level paradigm.