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 ϵr⪅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. Various topological fermionic excitations can be realized in two-dimensional materials. Here, the authors theoretically show that for slightly charge-doped bilayer graphene, an anomalous Hall crystal becomes the ground state at a suitable carrier density and relative dielectric constant.