Localized eigenstates in dodecagonal twisted bilayer graphene

Dodecagonal quasicrystalline order has been experimentally demonstrated in twisted bilayer graphene systems. In this talk, we report emergence of localized eigenstates in the dodecagonal quasicrystals without additional random disorder. That is to say, the non-periodic quasicrystalline order causes the localization. These localized states are evidenced by the scaling behaviors of inverse participation ratio and energy level statistics, which have been used to characterize Anderson localization phenomena. Using exact diagonalization method, we show that the localization can be driven by increasing the interlayer coupling strength. In addition, we will compare our result with the conventional two-dimensional Anderson localization transitions.