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The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking2–6. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation7–9. So far, FQAHE has been observed only in twisted MoTe2at a moiré filling factor v> 1/2 (refs. 10–13). Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene–hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance Rxy=hve2at v= 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxyequals 2he2at v= 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields14–16. By tuning the gate-displacement field Dand v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. Our system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field7–9,17–19, especially considering a lateral junction between FQAHE and superconducting regions in the same device20–22.

The emergence of moiré materials with flat bands provides a platform to systematically investigate and precisely control the correlated electronic phases. Here we report on a rich phase diagram of interpenetrating Hofstadter states—also called Chern insulators—and electron solids in a twisted WSe2/MoSe2heterobilayer using local electronic compressibility measurements. We show that this reflects the presence of both flat and dispersive moiré bands whose relative energies, and therefore occupations, are tuned by the density and magnetic field. At low density, the competition between moiré bands leads to a transition from the commensurate arrangements of singlets at doubly occupied sites to triplet configurations at high fields. Hofstadter states are generally favoured at high density as dispersive bands are populated, but are suppressed by an intervening region of re-entrant charge-ordered states in which holes originating from multiple bands cooperatively crystallize. Our results reveal the key microscopic ingredients that favour distinct correlated ground states in semiconductor moiré systems, and they demonstrate an emergent lattice model system in which both interactions and band dispersion can be experimentally controlled.