Bernal-stacked bilayer graphene modulated by a superlattice potential is a highly tunable system predicted to realize isolated topological flat bands. In this work we calculate the band structure and quantum geometry of bilayer graphene subject to both triangular and square superlattice potentials across a wide range of gate voltages. We identify the parameter regime that optimizes the “single-particle indicators” for the stability of a fractional Chern insulator (FCI) when a topological flat band is partially filled. Our results guide the quest for an experimental realization of an FCI in this platform.

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• Berry curvature
• Electronic structure
• Flat bands
• Fractionalization
• Quantum anomalous Hall effect
• Topological insulators
• Topological materials
• Topological phase transition
• Bilayer graphene
• Bloch wave theory