Orbital magnetic states in moiré graphene systems

Moiré graphene systems have attracted considerable attention in the past 3 years because they exhibit exotic phenomena including correlated insulating states, unconventional superconductivity and the quantum anomalous Hall effect. All these phenomena are intimately related to the valley-spin-degenerate and topologically non-trivial flat bands in moiré graphene systems. When time-reversal symmetry is broken spontaneously, such flavour-degenerate topological flat bands exhibit unconventional orbital magnetism associated with real-space current-loop patterns on the moiré length scale. In this Perspective, we first survey key experimental progress on the correlated insulating states and the quantum anomalous Hall phenomena. Most of these phenomena are related to the moiré orbital magnetic states, which originate from the topological nature of the moiré flat bands. Finally, we discuss theoretical progress in the understanding of the correlated insulating and quantum anomalous Hall phenomena from the perspective of spontaneous symmetry breaking.