On the nature of the correlated insulator states in twisted bilayer graphene

We use self-consistent Hartree-Fock calculations performed in the full $\pi$-band Hilbert space to assess the nature of the recently discovered correlated insulator states in magic-angle twisted bilayer graphene (TBG). In single spin/valley-flavor models we find two closely competing gapped states, one of which breaks the system's valley projected ${\cal C}_{2}{\cal T}$ symmetry and produces moir\'e bands with finite Chern numbers. Broken spin/valley flavor symmetries then enable gapped states to form not only at neutrality but also at total moir\'e band filling $n = \pm p/4$ with integer $p = -3, ..., 3$. We predict that the magic-angle TBG insulating states at $n = \pm 1/4$ and $n = \pm 3/4$ can exhibit a quantized anomalous Hall effect.