Kagome and Honeycomb flat bands in moire graphene systems

We propose a class of graphene-based moire systems hosting flat bands on kagome and honeycomb moire superlattices. These systems are formed by inducing approximate Kekule lattice periods in graphene moire systems, for instance, graphene layer stacked on a 2D substrate with lattice constant approximately square root three times that of graphene. When the moiré potentials are induced by a 2D irreducible corepresentation in the substrate, the model shows a rich phase diagram of low energy bands including eigenvalue fragile phases as well as kagome and honeycomb flat bands. A particularly interesting system is twisted bilayer Kekule graphene (graphene with a Kekule order), in which a pair of Kagome flat bands emerge around charge neutrality. The addition of spin-orbit coupling (from substrate, etc) can further lift symmetry protected degeneracies and create spin Chern bands. These systems provide promising new platforms for studying novel strongly correlated phases of matter.