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

Abstract

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 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.

5 pages plus supplemental material. Commenst are welcomed

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Cited by in corpus (6)

• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
• Electronic band structure and pinning of Fermi energy to van Hove singularities in twisted bilayer graphene: a self consistent approach
• Effective Floquet Hamiltonians for periodically-driven twisted bilayer graphene
• Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene
• Functional renormalization group for a large moiré unit cell