Switchable Chern insulator, isospin competitions and charge density\n waves in rhombohedral graphene moire superlattices

Graphene-based moire superlattices provide a versatile platform for exploring\nnovel correlated and topological electronic states, driven by enhanced Coulomb\ninteractions within flat bands. The intrinsic tunability of graphene s multiple\ndegrees of freedom enables precise control over these complex quantum phases.\nIn this study, we observe a range of competing phases and their transitions in\nrhombohedrally stacked hexalayer graphene on hexagonal boron nitride (r-6G/hBN)\nmoire superlattices. When electrons are polarized away from the moire\nsuperlattice, we firstly identify a Chern insulator with reversible Chern\nnumbers at v = 1 (one electron per moire cell), attributed to the competition\nbetween bulk and edge magnetizations.Then, we detect transitions between three\ndistinct insulating states at v = 2, driven by vertical displacement field D\nand vertical magnetic field B. These insulating phases are distinguished as\nspin-antiferromagnetic, spin-polarized, and valley-polarized insulators, based\non their responses to parallel and perpendicular magnetic fields. When\nelectrons are polarized toward the moire superlattice, in a device with large\ntwist angle, insulating states appear at v = 1/3 and 2/3 at zero magnetic\nfield, and v = 1/2 in a magnetic field. Our findings reveal a rich interplay of\ncharge, isospin, topology and magnetic field in rhombohedral graphene moire\nsuperlattices.\n