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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

Junkai Dong (董焌锴)1,*, Taige Wang2,3,*, Tianle Wang2,3,*, Tomohiro Soejima (副島智大)1, Michael P. Zaletel2,3, Ashvin Vishwanath1, and Daniel E. Parker2

  • *These authors contributed equally to this work.
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Phys. Rev. Lett. 133, 206503 – Published 12 November, 2024

DOI: https://doi.org/10.1103/PhysRevLett.133.206503

Abstract

Recent experiments on rhombohedral pentalayer graphene with a substrate-induced moiré potential have identified both Chern insulators and fractional quantum Hall states at zero magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moiré lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles, we study a model of interacting electrons in this geometry. Within self-consistent Hartree-Fock (SCHF) calculations, we find an isolated Chern band with small bandwidth and good quantum geometry. Exact diagonalization and density-matrix renormalization group calculations both confirm the band hosts fractional quantum Hall states without a magnetic field. Remarkably, the Chern band is stable at a wide range of angles, at four through six rhombohedral layers, at varying rhombohedral hopping parameters, and—most strikingly—survives in SCHF calculations when the moiré potential vanishes. In this limit, the state spontaneously breaks time-reversal and translation symmetry simultaneously, giving a topological crystalline state that we term the “anomalous Hall crystal.” We argue this is a general mechanism to create stable Chern bands in rhombohedral multilayer graphene, opening the door to studying the interplay between electronic topology, fractionalization, and spontaneous translation symmetry breaking.

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See Also

Theory of Quantum Anomalous Hall Phases in Pentalayer Rhombohedral Graphene Moiré Structures

Zhihuan Dong, Adarsh S. Patri, and T. Senthil
Phys. Rev. Lett. 133, 206502 (2024)

Fractional Quantum Anomalous Hall Effect in Rhombohedral Multilayer Graphene in the Moiréless Limit

Boran Zhou, Hui Yang, and Ya-Hui Zhang
Phys. Rev. Lett. 133, 206504 (2024)

Anomalous Hall crystals in rhombohedral multilayer graphene. II. General mechanism and a minimal model

Tomohiro Soejima (副島智大), Junkai Dong (董焌锴), Taige Wang, Tianle Wang, Michael P. Zaletel, Ashvin Vishwanath, and Daniel E. Parker
Phys. Rev. B 110, 205124 (2024)

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Phys. Rev. Lett. 133, 206503– Published 12 November, 2024
  • Received 20 November 2023
  • Revised 6 April 2024
  • Accepted 14 August 2024
Article part of CHORUS
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