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). 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 ${\mathcal{C}}_2\mathcal{T}$ symmetry. Broken spin/valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moir'e band filling $n=\pm p\mathrm{/}4$ 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 $\sim 20$, the gapped states do not necessarily break \CT symmetry and as a consequence the insulating states at $n=\pm 1\mathrm{/}4$ and $n=\pm 3\mathrm{/}4$ need not exhibit a quantized anomalous Hall effect.