Anomalous Hall Crystals in Rhombohedral Multilayer Graphene: Theory and a Simple Model

Wigner predicted in the 1930s that dilute electron gas can spontaneously break translation symmetry to give rise to a "Wigner crystal" [1], which has since been observed in many experiments. In contrast, a topological variant of Wigner crystals that carry nonzero Chern number --- Hall crystals [2, 3, 4, 5] --- have never been observed.We propose that a recent discovery of integer and fractional Chern insulators in rhombohedral multilayer graphene(RMG) [6] can be understood as an anomalous Hall crystal stabilized by a moire potential. We establish this by performing self-consistent Hartree-Fock calculation for RMG Hamiltonian [7].We next ask what stabilizes such a nontrivial crystalline state. To this end, we construct a simple phenomenological model called the "three-patch model". The model reveals that nontrivial spinors of the RMG are responsible for stabilizing the AHC state [8].

[1] Wigner, E. Phys. Rev. (1934)

[2] Kivelson, Kallin, Arovas, and Schrieffer. Phys. Rev. Lett. (1986)

[3] Halperin, Tesanovic, and Axel. Phys. Rev. Lett. (1986)

[4] Kivelson, Kallin, Arovas, and Schrieffer. Phys. Rev. B (1987)

[5] Tesanovic, Axel, and Halperin Phys. Rev. B (1989)

[6] Lu, Han, Yao et al. arXiv:2309.17436

[7] Dong, Wang, Wang et al. arXiv:2311.05568

[8] Soejima, Dong et al. arXiv:2403.05522

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