Fractional Chern insulators in magic-angle twisted bilayer graphene in the Hofstadter regime*

We apply a perpendicular magnetic field to the minimal effective two-orbital Fermi-Hubbard
model describing the low-energy physics of twisted bilayer graphene at the first magic angle. Through
the use of a Peierl’s substitution, we determine the Landau level splitting and study the structure of
the resulting Chern sub-bands for a range of magnetic flux per plaquette. We identify the minimal examples
of low-energy topological flat sub-bands in this framework. We show that, with the inclusion of a
density-density interaction, fractional Chern insulator states can be realized solely within these flat bands.
Specifically, we characterize the ν = 1/3 Laughlin state through the use of change pumping, spectral flow,
entanglement scaling, and CFT edge state counting; and we analyze its dependence on band flatness.
Ultimately, we comment on the requirements for the observation of fractional Chern insulators for this
system in experiment.