Interacting Valley Chern Insulator in Moiré Systems*

One salient feature of systems with Moiré superlattice is that the 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 Moiré potential. Then a Moiré system with a well-defined valley Chern number can become a nonchiral topological insulator with U(1) × Z_3 symmetry and a Z classification at the free fermion level. Here we demonstrate that the strongly interacting nature of the Moiré system reduces the classification of the valley Chern insulator from Z to Z_3, which is very different from the previously known examples of interaction reduced classification of topological insulators. We also show that an interacting valley Chern insulator is topologically equivalent to a bosonic symmetry protected topological state made of local boson operators. The effect of this interaction influenced classification is estimated in experimental systems.