The fractional quantum anomalous Hall effect (FQAHE), the analog of the fractional quantum Hall effect at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking. The demonstration of FQAHE could lead to non-Abelian anyons which form the basis of topological quantum computation. Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and high electron mobility. In this talk, I will 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 = h/(ve2) at moiré filling factors v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5, all within the Jain sequence of fractional quantum Hall states. In addition, at zero magnetic field, Rxy =2h/e2 near v = 1/2 and it varies linearly as the filling factor is tuned—similar to the composite Fermi liquid (CFL) in the half-filled lowest Landau level at high magnetic fields. 

 In addition to FQAHE induced by the moire effect, I will report the observation of integer quantum anomalous Hall effect in pentalayer graphene without a moire effect. This state features a Chern number C=5 and a distinct mechanism from those of magnetic topological insulators and 2D moire superlattice materials. We believe that the spin-orbital-coupling from the neighboring WS2 plays a key role in deciding the IQAH ground state.

The rich family of FQAH and IQAH states in our high-quality graphene provide an ideal platform for exploring charge fractionalization and exotic quasiparticles for topological quantum computation.