Interaction-driven Chern insulator at zero electric field in ABCB-stacked tetralayer graphene

ABCB-stacked tetralayer graphene, with intrinsic spontaneous polarization, offers a unique platform to explore electron correlation effects, whose interplay with spin-orbit coupling may engender topological phases. Here, employing a $\mathbf{k}\cdot\mathbf{p}$ model with self-consistent Hartree-Fock calculations, we investigate its electronic ground states. Remarkably, we find that the intrinsic polarization, in conjunction with strong interactions ($U=8 \text{ eV}$) and SOC, is sufficient to drive a $C=3$ quantum anomalous Hall state, obviating the need for an external electric field typical in ABCA stacks. Conversely, at moderate interactions ($U=6 \text{ eV}$), a minimal electric field is necessary. Furthermore, calculations predict other correlation-driven metallic phases such as quarter- and three-quarter-filled states. These results establish that the synergy of intrinsic polarization, correlations, and SOC governs the rich topological phenomena, suggesting ABCB-stacked graphene as a highly tunable platform for exploring emergent topological phenomena.