Quantum geometry of bilayer graphene with a superlattice potential

Bernal-stacked bilayer graphene subject to a spatially modulated "superlattice" potential (sBLG) exhibits topological flat bands with a valley Chern number. In this talk, we study the quantum geometry of sBLG. We compute the Chern number and fluctuations of the quantum geometric tensor of sBLG with respect to the external, tunable, superlattice potential and spatially uniform displacement potential. We identify a range of parameters that give rise to flat bands with a non trivial Chern number and comment on the "idealness" of these bands. Our results predict the optimal region of the phase diagram to search for a fractional Chern insulator.