Correlated phases and topological phase transition in twisted bilayer graphene at one quantum of magnetic flux

When the perpendicular magnetic flux per unit cell in a crystal is equal to the quantum of the magnetic flux, Φ₀=h/e, we enter the ``Hofstadter regime.'' The large unit cell of moir\'e materials such as magic-angle twisted bilayer graphene (MATBG) allows the experimental study of this regime at feasible values of the field around 20 to 30 T. In this work, we report the numerical analysis of a tight-binding model for MATBG at one quantum of external magnetic flux, including the long-range Coulomb and on-site Hubbard interaction. We study the correlated states for dopings of -2,0, and 2 electrons per unit cell at the mean-field level. We find competing insulators with Chern numbers 2 and 0 at positive doping, the stability of which is determined by the dielectric screening, which opens up the possibility of observing a topological phase transition in this system.