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

Abstract

We use self-consistent Hartree-Fock calculations performed in the full\n$\\pi$-band Hilbert space to assess the nature of the recently discovered\ncorrelated insulator states in magic-angle twisted bilayer graphene (TBG). We\nfind that gaps between the flat conduction and valence bands open at neutrality\nover a wide range of twist angles, sometimes without breaking the system's\nvalley projected ${\\cal C}_{2}{\\cal T}$ symmetry. Broken spin/valley flavor\nsymmetries then enable gapped states to form not only at neutrality, but also\nat total moir\\'e band filling $n = \\pm p/4$ with integer $p = 1, 2, 3$, when\nthe twist angle is close to the magic value at which the flat bands are most\nnarrow. Because the magic-angle flat band quasiparticles are isolated from\nremote band quasiparticles only for effective dielectric constants larger than\n$ \\sim 20$, the gapped states do not necessarily break \\CT symmetry and as a\nconsequence the insulating states at $n = \\pm 1/4$ and $n = \\pm 3/4$ need not\nexhibit a quantized anomalous Hall effect.\n