Abstract

The recently synthesized 30° twisted bilayer graphene (30°-TBG) systems are unique quasicrystal systems possessing dodecagonal symmetry with graphene’s relativistic properties. The authors employ a real-space numerical atomistic framework that respects both the dodecagonal rotational symmetry and the massless Dirac nature of the electrons to describe the local density of states of the system. The approach is efficient for systems with very large unit cells and does not rely on periodic boundary conditions. These features allow the authors to address a broad class of multilayer two-dimensional crystals with incommensurate configurations, particularly TBGs. Their results reveal that the 30°-TBG electronic spectrum consists of extended states together with a set of localized wave functions. The localized states exhibit fractal patterns consistent with the quasicrystal tiling.

Abstract

The recently synthesized 30° twisted bilayer graphene (30°-TBG) systems are unique quasicrystal systems possessing dodecagonal symmetry with graphene’s relativistic properties. The authors employ a real-space numerical atomistic framework that respects both the dodecagonal rotational symmetry and the massless Dirac nature of the electrons to describe the local density of states of the system. The approach is efficient for systems with very large unit cells and does not rely on periodic boundary conditions. These features allow the authors to address a broad class of multilayer two-dimensional crystals with incommensurate configurations, particularly TBGs. Their results reveal that the 30°-TBG electronic spectrum consists of extended states together with a set of localized wave functions. The localized states exhibit fractal patterns consistent with the quasicrystal tiling.

Abstract

The recently synthesized 30° twisted bilayer graphene (30°-TBG) systems are unique quasicrystal systems possessing dodecagonal symmetry with graphene’s relativistic properties. The authors employ a real-space numerical atomistic framework that respects both the dodecagonal rotational symmetry and the massless Dirac nature of the electrons to describe the local density of states of the system. The approach is efficient for systems with very large unit cells and does not rely on periodic boundary conditions. These features allow the authors to address a broad class of multilayer two-dimensional crystals with incommensurate configurations, particularly TBGs. Their results reveal that the 30°-TBG electronic spectrum consists of extended states together with a set of localized wave functions. The localized states exhibit fractal patterns consistent with the quasicrystal tiling.

Abstract

The recently synthesized 30° twisted bilayer graphene (30°-TBG) systems are unique quasicrystal systems possessing dodecagonal symmetry with graphene’s relativistic properties. The authors employ a real-space numerical atomistic framework that respects both the dodecagonal rotational symmetry and the massless Dirac nature of the electrons to describe the local density of states of the system. The approach is efficient for systems with very large unit cells and does not rely on periodic boundary conditions. These features allow the authors to address a broad class of multilayer two-dimensional crystals with incommensurate configurations, particularly TBGs. Their results reveal that the 30°-TBG electronic spectrum consists of extended states together with a set of localized wave functions. The localized states exhibit fractal patterns consistent with the quasicrystal tiling.