Emergent $\text{D}_6$ symmetry in fully-relaxed magic-angle twisted bilayer graphene

Understand

We present a tight-binding calculation of a twisted bilayer graphene at magic angle $\theta\sim 1.08^\circ$, allowing for full, in- and out-of-plane, relaxation of the atomic positions.

• The resulting band structure displays as usual four narrow mini bands around the neutrality point, well separated from all other bands after the lattice relaxation.
• A thorough analysis of the mini-bands Bloch functions reveals an emergent $D_6$ symmetry, despite the lack of any manifest point group symmetry in the relaxed lattice.
• The Bloch functions at the $\Gamma$ point are degenerate in pairs, reflecting the so-called valley degeneracy.