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

We use self-consistent Hartree-Fock calculations performed in the full π-band Hilbert space to assess the nature of the recently discovered correlated insulator states in magic-angle twisted bilayer graphene (MATBG). We show that at integer number of electrons per moiré period, the mean-field ground states break the combined two-fold rotation and time reversal symmetry $C_2T$ that protects the moiré-band Dirac points, inducing gaps and establishing valley projected bands that have non-zero Chern numbers. Broken spin/valley flavor symmetries then enable gapped states to form not only at neutrality but also at moiré band filling n = ±p/4, where p is the number of electrons per moiré period. We predict that the MATBG ground states at n = ±1/4 and n = ±3/4 have an anomalous Hall effect, and discuss the implications of our findings for theories of magic-angle superconductivity.