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M. Angeli, D. Mandelli, A. Valli, A. Amaricci, M. Capone, E. Tosatti, M. Fabrizio:
"Emergent D₆ symmetry in fully relaxed magic-angle twisted bilayer graphene";
Physical Review B, 98 (2018), S. 235137-1 - 235137-8.

We present a tight-binding calculation of a twisted bilayer graphene at magic angle θ ~ 1.08 °, allowing for full, in- and out-of-plane, relaxation of the atomic positions. The resulting band structure displays, as usual, four narrow minibands around the neutrality point, well separated from all other bands after the lattice relaxation. A thorough analysis of the miniband Bloch functions reveals an emergent D₆ symmetry, despite the lack of any manifest point-group symmetry in the relaxed lattice. The Bloch functions at the Γ point are degenerate in pairs, reflecting the so-called valley degeneracy. Moreover, each of them is invariant under C_3z, i.e., transforming like a one-dimensional, in-plane symmetric irreducible representation of an "emergent" D₆ group. Out of plane, the lower doublet is even under C_2x, while the upper doublet is odd, which implies that at least eight Wannier orbitals, two s-like and two p_z-like ones for each of the supercell sublattices AB and BA, are necessary but probably not sufficient to describe the four minibands. This unexpected one-electron complexity is likely to play an important role in the still unexplained metal-insulator-superconductor phenomenology of this system.

Band gap; First-principles calculations; Mechanical deformation; 2-dimensional systems; Electronic structure; Graphene; Strongly correlated systems; Band structure methods; Continuous symmetries in condensed matter; Tight-binding model; Wannier function

http://dx.doi.org/10.1103/PhysRevB.98.235137