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

Tomohiro Soejima (副島智大)1,*, Junkai Dong (董焌锴)1,*, Taige Wang2,3,4, Tianle Wang2,3, Michael P. Zaletel2,3, Ashvin Vishwanath1, and Daniel E. Parker2,5

  • *These authors contributed equally to this work.
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Phys. Rev. B 110, 205124 – Published 12 November, 2024

DOI: https://doi.org/10.1103/PhysRevB.110.205124

Abstract

We propose a minimal “three-patch model” for the anomalous Hall crystal (AHC), a topological electronic state that spontaneously breaks both time-reversal symmetry and continuous translation symmetry. The proposal for this state is inspired by the recently observed integer and fractional quantum Hall states in rhombohedral multilayer graphene at zero magnetic field. There, interaction effects appear to amplify the effects of a weak moiré potential, leading to the formation of stable, isolated Chern bands. It has been further shown that Chern bands are stabilized in mean-field calculations even without a moiré potential, enabling a realization of the AHC state. Our model is built on the dissection of the Brillouin zone into patches centered around high-symmetry points. Within this model, the wave functions at high-symmetry points fully determine the topology and energetics of the state. We extract two quantum geometrical phases of the noninteracting wave functions that control the stability of the topologically nontrivial AHC state. The model predicts that the AHC state wins over the topological trivial Wigner crystal in a wide range of parameters, and agrees very well with the results of full self-consistent Hartree-Fock calculations of the rhombohedral multilayer graphene Hamiltonian.

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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)

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), Taige Wang, Tianle Wang, Tomohiro Soejima (副島智大), Michael P. Zaletel, Ashvin Vishwanath, and Daniel E. Parker
Phys. Rev. Lett. 133, 206503 (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)

Article Text

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Phys. Rev. B 110, 205124– Published 12 November, 2024
  • Received 12 April 2024
  • Revised 12 August 2024
  • Accepted 13 August 2024
Article part of CHORUS
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