In this talk, we will discuss correlated and topological states emerging from slightly carrier doped rhombohedral multilayer graphene (RMG) systems. First, we develop a beyond-mean-field theoretical framework to study the Winger-crystal transition problem in slightly charge-doped RMG [1]. Notably, we find that bilayer graphene may be a promising candidate to realize the peculiar anomalous Hall crystal state, which is predicted to be the interacting ground state when the carrier density is below Counter intuitively, such topological anomalous Hall crystal becomes more stable than the trivial Wigner crystal due to the lower correlation energy gained from dynamical charge fluctuations [1]. Second, we consider RMG in the “transdimensional regime”, the thickness of which is much larger than a single atomic layer, yet smaller than or comparable to vertical mean free path. In this regime, we report the discovery of a new class of bulk Fermi surface structure with unprecedented low symmetry, the “Fermi lun”, with peculiar crescent shaped Fermi energy contours [2]. This emergent Fermi-lune state driven by electron-electron interactions spontaneously breaks time-reversal, mirror, and rotational symmetries, leading to two distinctive phenomena: giant intrinsic non-reciprocity in longitudinal transport and a new type of magnetism termed “transdimensional orbital magnetism” [2]. The latter is manifested as a fundamentally new type of anomalous Hall effect that exhibits hysteretic responses to in-plane magnetic fields [3]. Lastly, if time allows, I will discuss fractional topological states emerging from RMG coupled with kagome patterned dielectric superlattice [4].

[1] Z. Guo, J. Liu, arXiv:2409.14658 [2] M. Li et al., arXiv:2505.05414

[3] Q. Li et al., arXiv:2505.03891 [4] Y. Shi et al., arXiv:2502.17320