Data used in "Fractional Topological States in Rhombohedral Multilayer Graphene Modulated by Kagome Superlattice"

Fractional quantum anomalous Hall effects realized in twisted bilayer MoTe2 and multilayer graphene-based moire heterostructures have captured a tremendous growth of interest. In this Letter, we propose that rhombohedral multilayer graphene coupled with an artificial kagome superlattice potential is a new platform to realize various fractional topological phases. Taking Bernal bilayer graphene as the simplest example, when it is placed on top of a prepatterned SiO2 substrate with periodic arrays of holes arranged into kagome lattice, the system would be subject to a tunable kagome superlattice potential once an electrostatic voltage drop between the top and bottom gates is applied. Then, we theoretically study the electronic band structures, topological properties, and quantum geometric properties of the Bloch states of Bernal bilayer graphene coupled with a realistic kagome superlattice potential, which is well benchmarked by transport measurements in the weak superlattice-potential regime. We find that the system may exhibit nearly ideal topological f lat bands in a substantial region of the parameter space spanned by superlattice constant and electrostatic potential strength. When these topological flat bands are fractionally filled, exact diagonalization calculations suggest that the system would exhibit rich fractional topological phases at 1/3, 2/3, 2/5, 3/5 and 1/2 fillings including both fractional Chern insulators and anomalous composite Fermi liquids under zero magnetic field. We also find that Halperin-type FCI states may emerge from the Chern-number-2 flat bands of trilayer graphene coupled with kagome superlattice potential.