Fractional Chern mosaic in supermoir\'e graphene

We propose the realization of a fractional Chern mosaic: a state characterized by a spatially varying topological order. This state is enabled by a separation of length scales that emerges when three graphene sheets are sequentially rotated by a small twist angle. The resulting structure features not only conventional moir\'e lattices, but also a much larger supermoir\'e lattice. We demonstrate that a fractional Chern mosaic arises when electron correlations induce fractionalization locally on the moir\'e scale, while the pattern of fractionalization varies at the supermoir\'e scale.