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

Ming Xie; Allan H. MacDonald

doi:10.1103/PhysRevLett.124.097601

paper

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

arXiv:1812.04213 · doi:10.1103/PhysRevLett.124.097601

Abstract

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 $C_{2} T$ symmetry. Broken spin/valley flavor symmetries then enable gapped states to form not only at neutrality, but also at total moiré band filling $n = \pm p /4$ 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 $\sim 20$ , the gapped states do not necessarily break \CT symmetry and as a consequence the insulating states at $n = \pm 1/4$ and $n = \pm 3/4$ need not exhibit a quantized anomalous Hall effect.

arXiv comment5 pages plus supplemental material. Commenst are welcomed

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

Abstract

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