Quantum anomalous Hall crystals in moiré bands with higher Chern number

Abstract

The realization of fractional Chern insulators in moiré 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 moiré 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.

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Cited by in corpus (5)

• Quantum anomalous Hall effects and emergent $\mathrm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene
• Generic integer and fractional quantum anomalous Hall crystals from interaction-driven band folding
• Exciton fractional Chern insulators in moiré heterostructures
• Topological Order Without Band Topology in Moiré Graphene
• Direct visualization of gate-tunable flat bands in twisted double bilayer graphene