Correlation stabilized anomalous Hall crystal in bilayer graphene

At low carrier densities, interacting electrons can form a Wigner crystal. Rhombohedral multilayer graphene hosts high-order Dirac fermions with nontrivial Berry phases. Using a beyond-mean-field theoretical framework, here we study the ground states of slightly charge-doped rhombohedral multilayer graphene under vertical displacement field. We find a Fermi liquid to trivial Wigner crystal transition at critical densities of ~1-2 × 10¹¹ cm^-2, which generally increase with displacement field and layer number. Notably, an anomalous Hall crystal with spontaneous quantized anomalous Hall conductivity emerges at lower densities ~2 × 10¹⁰ cm^-2 and for dielectric constants ϵ_r⪅5. This topological anomalous Hall crystal is stabilized over the trivial Wigner crystal due to lower correlation energy gained from dynamical charge fluctuations. Our work identifies slightly carrier-doped bilayer graphene as a promising candidate for realizing the anomalous Hall crystal. Moreover, our method can be readily applied to other interacting 2D systems including moiré superlattices.