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The quantum anomalous Hall (QAH) effect, first proposed by the Haldane model,has become a paradigmatic example of application of band topology to condensedmatter physics. The recent experimental discoveries of high Chern number QAHeffect in pentalayer and tetralayer rhombohedral graphene highlights theintriguing interplay between strong interactions and spin-orbit coupling (SOC).Here we propose a minimal interacting model for spin-orbit coupled rhombohedralgraphene and use the Hartree-Fock analysis to explore the phase diagram atcharge neutrality. We find that with Ising SOC on one outmost graphene layer,the in-plane layer-antiferromagnetic order is the insulating ground statewithout displacement field. Upon increasing the gate displacement field, wefind that the QAH state with Chern number being equal to the layer numberemerges between layer-antiferromagentic state and layer-polarized state, whichis consistent with experimental observations. We further study phase diagramfor different thickness and find pentalayer is optimal for the QAH effect.Finally, we predict that QAH state is enlarged by engineering opposite IsingSOC on the opposite outmost layers of rhombohedral graphene.

Layer-Dependent Quantum Anomalous Hall Effect in Rhombohedral Graphene