Layer-Dependent Quantum Anomalous Hall Effect in Rhombohedral Graphene (2401.13413v2)

Abstract: The quantum anomalous Hall (QAH) effect, first proposed in the Haldane model, is a paradigmatic example of the application of band topology in condensed matter physics. The recent experimental discoveries of high Chern number QAH effect in pentalayer and tetralayer rhombohedral graphene highlight the intriguing interplay between strong interactions and spin-orbit coupling (SOC). Here we propose a minimal interacting model for spin-orbit-coupled rhombohedral graphene and use the Hartree-Fock analysis to explore the phase diagram at charge neutrality. We find that with Ising SOC on one outmost graphene layer, the in-plane layer-antiferromagnetic order is the insulating ground state without displacement field. Upon increasing the gate displacement field, we find that the QAH state with Chern number being equal to the layer number emerges between layer-antiferromagnetic state and layer-polarized state, which is consistent with experimental observations. Remarkably, we study the phase diagram for different thicknesses and find pentalayer is optimal for the QAH effect. Finally, we propose that the QAH state is enlarged by engineering opposite Ising SOC on the opposite outmost layers of rhombohedral graphene. These results will facilitate the realization of QAH states in rhombohedral graphene with different thicknesses. Our work serves as a foundation for further exploration of correlated physics of insulating state in rhombohedral graphene.