Lowest-energy Moiré Band Formed by Dirac Zero Modes in Twisted Bilayer Graphene

Abstract

An unconventional insulating phase and a superconducting phase were recently discovered in the twisted bilayer graphene [Y. Cao et al, Nature {\bf 556}, 80; {\bf 556}, 43 (2018)], but the relevant low-energy electronic states have not been clearly identified yet. In this work, I show that the interlayer hopping induces a spatially modulated Dirac mass term in the continuum Hamiltonian, and leads to a low-energy band formed by Dirac zero modes in the moiré superlattice. This moiré band becomes extremely flat and thus strongly correlated as the Dirac velocity vanishes at the magic angle, and enters a quantum disordered Mott insulating phase at $1/4$ and $3/4$ filling, i.e., $\pm 2$ excess electrons per moiré supercell, which may account for the insulating phase discovered in experiments.

arXiv comment4 pages, 1 figure

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• Superconductivity from Valley Fluctuations and Approximate SO(4) Symmetry in a Weak Coupling Theory of Twisted Bilayer Graphene
• The Landau Level of Fragile Topology
• Internal screening and dielectric engineering in magic-angle twisted bilayer graphene
• Is magic-angle twisted bilayer graphene near a quantum critical point?
• Nematicity with a twist: rotational symmetry breaking in a moiré superlattice
• Topological flat bands in twisted trilayer graphene
• The nature of correlations in the insulating states of twisted bilayer graphene
• Floquet-Engineered Topological Flat Bands in Irradiated Twisted Bilayer Graphene
• Magic-Angle Semimetals with Chiral Symmetry
• Nematic superconductivity in magic-angle twisted bilayer graphene from atomistic modeling
• Metal-insulator transition and dominant $d+id$ pairing symmetry in twisted bilayer graphene
• Enhanced correlations and superconductivity in weakly interacting partially flat band systems: a determinantal quantum Monte Carlo study
• Possible nodeless $s^{\pm }$-wave superconductivity in twisted bilayer graphene
• Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle-twisted bilayer-graphene
• Renormalized Magic Angles in Asymmetric Twisted Graphene Multilayers