Twisted bilayer graphene revisited: minimal two-band model for low-energy bands

Abstract

An accurate description of the low-energy electronic bands in twisted bilayer graphene (tBLG) is of great interest due to their relation to correlated electron phases, such as superconductivity and Mott-insulator behavior at half-filling. The paradigmatic model of Bistritzer and MacDonald [PNAS 108, 12233 (2011)], based on the moiré pattern formed by tBLG, predicts the existence of "magic angles" at which the Fermi velocity of the low-energy bands goes to zero, and the bands themselves become dispersionless. Here, we reexamine the low-energy bands of tBLG from the ab initio electronic structure perspective, motivated by features related to the atomic relaxation in the moiré pattern, namely circular regions of AA stacking, triangular regions of AB/BA stacking and domain walls separating the latter. We find that the bands are never perfectly flat and the Fermi velocity never vanishes, but rather a "magic range" exists where the lower band becomes extremely flat and the Fermi velocity attains a non-zero minimum value. We propose a simple $(2+2)$-band model, comprised of two different pairs of orbitals, both on a honeycomb lattice: the first pair represents the low-energy bands with high localization at the AA sites, while the second pair represents highly dispersive bands associated with domain-wall states. This model gives an accurate description of the low-energy bands with few (13) parameters which are physically motivated and vary smoothly in the magic range. In addition, we derive an effective two-band hamiltonian which also gives an accurate description of the low-energy bands. This minimal two-band model affords a connection to a Hubbard-like description of the occupancy of sub-bands and can be used a basis for exploring correlated states.

Accepted in Phys. Rev. B

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• Supercell Wannier functions and a faithful low-energy model for Bernal bilayer graphene
• Stacking-dependent electronic structure of ultrathin perovskite bilayers
• Diagrammatic perturbation approach to moiré bands in twisted bilayer graphene
• Polarization textures in crystal supercells with topological bands
• Nonflat bands and chiral symmetry in magic-angle twisted bilayer graphene
• Twisted bilayer graphene from first-principles: structural and electronic properties
• Wavefunction textures in twisted bilayer graphene from first principles
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Microscopic theory for electron-phonon coupling in twisted bilayer graphene