Fractional quantum anomalous Hall effect in multilayer graphene

Rhombohedral graphene (RG), with its unique electronic properties, has emerged as a versatile platform for exploring a wide range of topological and correlated phenomena. In its pristine form, RG hosts a pair of flat bands that touch at zero energy, giving rise to correlated electron phenomena, which can be further tuned by applying an electric field. Additionally, when electron correlation breaks isospin symmetry, the valley-dependent Berry phase at zero energy can lead to the formation of topologically non-trivial states. Recent studies have shown that multilayer RG can support exotic states, including superconductivity, correlated insulator, and Chern insulator. By placing transition metal dichalcogenides in proximity to RG, spin-orbit coupling can be induced, leading to the realization of the quantum anomalous Hall effect with a large Chern number (C = ±5) at temperatures up to 1.5 Kelvin, without the need for magnetic elements or moiré superlattices—this represents a significant departure from previous experimental approaches. Furthermore, aligning RG with an adjacent hexagonal boron nitride (hBN) layer to induce a moiré potential generates narrow minibands with non-trivial topology. In a pentalayer RG/hBN moiré superlattice, the fractional quantum anomalous Hall effect (FQAHE) has been observed at temperatures of a few hundred milli-Kelvin, sparking discussions regarding the underlying mechanisms and the influence of moiré effects. At even lower electron temperatures, two additional FQAH states and reduced longitudinal resistance (R_xx) have been observed in pentalayer RG/hBN moiré superlattices compared to previous reports. Simultaneously, a new extended quantum anomalous Hall (EQAH) state has been detected, characterized by a Hall resistance (R_xy) of h/e² and vanishing R_xx, spanning a wide range of filling factors (ν) from 0.5 to 1.3, coexisting with the FQAH states. The rich array of emergent quantum phenomena in the RG family, particularly the coexistence of FQAHE and superconductivity, offers an ideal platform for investigating charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field.