  The fractional quantum anomalous Hall effect (FQAHE), the analog of the
fractional quantum Hall effect1 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. So far, FQAHE has been observed only
in twisted MoTe2 (t-MoTe2) at moire filling factor v > 1/2. Graphene-based
moire 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 moire superlattice. At zero magnetic field, we observed plateaus
of quantized Hall resistance Rxy = h/(ve^2) at filling factors v = 1, 2/3, 3/5,
4/7, 4/9, 3/7 and 2/5 of the moire superlattice respectively. These features
are accompanied by clear dips in the longitudinal resistance Rxx. In addition,
at zero magnetic field, Rxy equals 2h/e^2 at v = 1/2 and varies linearly with
the filling factor-similar to the composite Fermi liquid (CFL) in the
half-filled lowest Landau level at high magnetic fields. By tuning the gate
displacement field D and v, we observed phase transitions from CFL and FQAH
states to other correlated electron states. Our graphene system provides an
ideal platform for exploring charge fractionalization and (non-Abelian) anyonic
braiding at zero magnetic field, especially considering a lateral junction
between FQAHE and superconducting regions in the same device.
