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.