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). 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 C2T symmetry. Broken spin-valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moire 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 similar to 20, the gapped states do not necessarily break C2T symmetry and as a consequence the insulating states at n = +/- 1/4 and n = +/- 3/4 need not exhibit a quantized anomalous Hall effect.