Strongly interacting phases in twisted bilayer graphene at the magic angle

Twisted graphene bilayers near the magic angle are known to have a cascade of insulating phases at integer filling factors of the low energy bands. In this Letter we address the nature of these phases through an unrestricted self-consistent Hartree-Fock calculation on the lattice that, for the first time, accounts for all electronic bands. Using numerically unbiased methods, we show that Coulomb interactions screened only by metallic gates produce ferromagnetic insulating states at integer fillings ν ∈ [−4,4] with maximal spin polarization MFM = 4 − |ν|. With exception of the ν = 0, −2 states, all other integer fillings have insulating phases with additional sublattice symmetry breaking and antiferromagnetism in the remote bands. Valley polarization is found away from half-filling. Odd filling factors |ν| = 1, 3 have anomalous quantum Hall states with Chern number |C| = 1, whereas the |ν| = 3 states show strong particle-hole asymmetry in the small gap regime, in agreement with experiments. We map the metal-insulator transitions of these phases as a function of the background dielectric constant.