  One salient feature of systems with Moir\'{e} superlattice is that, Chern
number of "minibands" originating from each valley of the original graphene
Brillouin zone becomes a well-defined quantized number because the miniband
from each valley can be isolated from the rest of the spectrum due to the
Moir\'{e} potential. Then a Moir\'{e} system with a well-defined valley Chern
number can become a nonchiral topological insulator with $U(1) \times Z_3 $
symmetry and a $\mathbb{Z}$ classification at the free fermion level. Here we
demonstrate that the strongly interacting nature of the Moir\'{e} system
reduces the classification of the valley Chern insulator from $\mathbb{Z}$ to
$\mathbb{Z}_3$, and it is topologically equivalent to a bosonic symmetry
protected topological state made of local boson operators. We also demonstrate
that, even if the system becomes a superconductor when doped away from the
valley Chern insulator, the valley Chern insulator still leaves a topological
imprint as the localized Majorana fermion zero mode in certain geometric
configuration.

Strongly Correlated Electrons