Abstract: 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
•  

Coffee, tea and cookies available in the third floor lounge at 2:45 pm.