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 (TBG). We find that gaps between the flat conduction and valence bands open at neutrality over a wide range of twist angles, sometimes without breaking the system's valley projected C₂ T symmetry. Broken spin/valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moir\'e band filling n = ± p/4 with integer $p = 1, 2, 3$, when the twist angle is close to the magic value at which the flat bands are most narrow. Because the magic-angle flat band quasiparticles are isolated from remote band quasiparticles only for effective dielectric constants larger than ~ 20, the gapped states do not necessarily break symmetry and as a consequence the insulating states at n = ± 1/4 and n = ± 3/4 need not exhibit a quantized anomalous Hall effect.