Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries
J. A. Crosse, Pilkyung Moon
Abstract
Twisted bilayer graphene with a twist angle 30\ifmmode^\circ\else\textdegree\fi{} is mapped onto a quasicrystal with a 12-fold rotational symmetry. The authors investigate the quasicrystalline electronic states for every possible two-dimensional twisted bilayer quasicrystal system. The quasicrystalline resonant interaction emerges at specific wave vectors from the combination of the rotational symmetry of the bilayers and the translational symmetries of the constituent layers, as long as all the dominant interlayer interactions occur between the atomic orbitals that have the same magnetic quantum number. In addition, the authors investigate the effects of lifting both interlayer and sublattice symmetry on the respective electronic structures.