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

Interacting Valley Chern Insulator and its Topological Imprint on Moir\'{e} Superconductors