  Fractional quantum anomalous hall effect (FQAHE), a transport effect with
fractionally quantized Hall plateau emerging under zero magnetic field,
provides a radically new opportunity to engineer topological quantum
electronics. By construction of topological flat band with moire engineering,
intrinsic FQAHE has been observed in twisted MoTe2 system and rhombohedral
pentalayer graphene/hBN moire superlattices with anomalous Hall resistivity
quantization number C <= 2/3 including the gapless composite Fermi-liquid state
with C = 1/2. Here we experimentally demonstrate a new system of rhombohedral
hexalayer graphene (RHG)/hBN moire superlattices showing both fractional and
integer quantum anomalous Hall effects when the lowest flat Chern band is
fractionally and fully filled at zero magnetic field. The zero-field Hall
resistance Rho_xy = h/Ce2 is quantized to values corresponding to C = 3/5, 2/3,
5/7, 3/4, 7/9 and 1 at moire filling factors v = 3/5, 2/3, 5/7, 3/4, 7/9 and 1,
respectively. Particularly, the C = 3/4 FQAHE state at v = 3/4 moire filling
featuring a minimum of longitudinal resistance Rho_xx and fractionally
quantized Hall resistance Rho_xy = 4h/3e2, is observed for the first time under
zero magnetic field. Such a state may be similar to the C = 3/4 fractional
quantum hall (FQHE) state recently observed at high magnetic fields9,10 and
possibly host fractional charge excitations obeying non-Abelian statistics. By
tuning the electrical and magnetic fields at 0 < v < 1, we have observed a sign
reversal of the Hall resistivity for v = 2/3 state, indicating a transition
from quasi-electron-like excitations to quasi-hole ones. Our experiment has
established RHG/hBN moire superlattices a promising platform to explore
quasi-particles with fractional charge excitations and non-Abelian anyons at
zero magnetic field.
