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Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
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abstract
Recent experiments on rhombohedral pentalayer graphene flakes with a substrate induced moir\'e potential have identified both Chern insulators and fractional Quantum Hall states in the absence of an applied magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moir\'e lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles we study an interacting model of electrons in this geometry, first within the self-consistent Hartree-Fock (SCHF) approximation. We find an isolated Chern band with Chern number $|C|=1$, that moreover is relatively flat and shows good quantum geometry. Exact diagonalization and density matrix renormalization group methods at fractional filling establish the presence of fractional quantum anomalous Hall (FQAH) states. The $|C|=1$ band in SCHF is remarkably robust to varying microscopic parameters, and is also found in the $N_L=4$ and $N_L=6$ layer systems. Remarkably, it appears stable even to switching off the moir\'e potential, pointing to spontaneous breaking of translation symmetry. We term this topological crystalline state the ``anomalous Hall crystal" (AHC), and argue that it constitutes a general mechanism for creating stable Chern bands in rhombohedral graphene. Our work elucidates the physics behind the recent rhombohedral pentalayer graphene observations, predicts the appearance of the same phase in other systems, and opens the door to studying the interplay between electronic topology and spontaneous translation symmetry breaking.
Forward citations
Cited by 6 Pith papers
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Continuum models for twisted MoTe2 and WSe2 are constructed directly from DFT by projecting the DFT Hamiltonian onto a basis of continuum-model terms, without nonlinear fitting.
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Continuous transition from Fermi liquid to A fractional Chern insulator
A critical theory is proposed for a continuous Fermi liquid to fractional Chern insulator transition at ν=2/3, predicting a high-temperature Hall resistivity near 3/2 h/e^2 on the Fermi liquid side.
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Quantum Geometry in the NbSe$_2$ Family I: Obstructed Compact Wannier Function and New Perturbation Theory
Monolayer NbSe2's Fermi-level flat band is an obstructed atomic band whose Wannier function is 94% reproduced by a compact three-site orbital, and its minimal model has next-nearest-neighbor hopping larger than neares...
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Switchable Chern insulator, isospin competitions and charge density waves in rhombohedral graphene moire superlattices
A rhombohedral hexalayer graphene/hBN moiré device hosts a doping-switchable Chern insulator, three competing isospin insulators at v=2, and charge-density-wave states at fractional fillings.
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Magnetorotons in Moir\'e Fractional Chern Insulators
Moiré fractional Chern insulators in twisted MoTe2 are predicted to host universal finite-momentum magnetorotons, whose long-wavelength limit is a gapped chiral angular-momentum-2 geometric excitation.
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Quantum Geometry in Quantum Materials
This review surveys how the quantum geometric tensor shapes superconductivity, spin stiffness, exciton condensates, Landau levels, and fractional Chern insulators in quantum materials.
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