Topological electronic crystals (TECs) are electronic phases of matter where spontaneous crystalline order coexists with, or indeed gives rise to, a quantized topological response. TECs are currently of great interest due to recent discoveries in moiré materials of quantized (anomalous) Hall responses over extended ranges of density, indicating that they– and their fractional descendants– can be stabilized [1,2]. However, TECs confound most beyond-mean-field numerical approaches, making exactly solvable models valuable. In this talk, we introduce a beyond-mean-field, analytically controlled theory of a class of TECs known as (anomalous) Hall crystals [3]. Our setup involves Landau levels or parent Chern bands subject to a one-dimensional periodic potential, mimicking aspects of moiré physics, with the system spontaneously forming charge density waves in the transverse direction, giving rise to various Chern numbers. We present a global phase diagram, contrast the Hall and anomalous Hall cases, and discuss experimental realizations. Finally, we present surprising aspects of magnetism in TECs distinguishing them sharply from ordinary Wigner crystals.
[1] Su et al., Topological electronic crystals in twisted bilayer-trilayer graphene, arXiv:2406.17766 [2] Lu et al., Extended Quantum Anomalous Hall States in Graphene/hBN Moiré Superlattices, arXiv:2408.10203 [3] NP, G. Shavit, L. Fu, Designing (higher) Hall crystals, arXiv:2410.03888
[2] Lu et al., Extended Quantum Anomalous Hall States in Graphene/hBN Moiré Superlattices, arXiv:2408.10203
[3] NP, G. Shavit, L. Fu, Designing (higher) Hall crystals, arXiv:2410.03888