Switchable Chern Insulators and Competing Quantum Phases in Rhombohedral Graphene Moiré Superlattices

Graphene-based moiré superlattices provide a versatile platform for exploring novel correlated and topological electronic states, driven by enhanced Coulomb interactions within flat bands. The intrinsic tunability of graphene's multiple degrees of freedom enables precise control over these complex quantum phases. In this study, we observe a range of competing phases and their transitions in rhombohedral stacked hexalayer graphene on hexagonal boron nitride (r-6G/hBN) moiré superlattices. When electrons are polarized away from the moiré superlattice, we first identify a Chern insulator with reversible Chern numbers at v=1 (one electron per moiré cell), revealing a competition between bulk and edge orbital magnetization. At v=2, three distinct insulating phases-spin-antiferromagnetic, spin-polarized, and valley-polarized-emerge under vertical displacement field D and magnetic field B_{⊥}, governed by hierarchical isospin symmetry breaking. Furthermore, charge density wave (CDW) states at ν=1/3 and 2/3, along with a magnetic-field-induced stripe phase at ν=1/2, demonstrate tunable correlated orders at fractional fillings. Our findings reveal a rich interplay of charge, isospin, topology, and magnetic field in rhombohedral graphene moiré superlattices.