Length scale formation in the Landau levels of quasicrystals

Exotic tiling patterns of quasicrystals have motivated extensive studies quantum phenomena such as critical states and phasons. Nevertheless, the systematic understanding Landau levels in presence magnetic field has not been established yet. One main obstacles is complication quasiperiodic tilings without periodic length scales, thus it thought that system cannot possess any universal features levels. In this paper, contrary to these assertions, we develop a generic theory for quasicrystals. Focusing on two dimensional with rotational symmetries, highlight induce anomalous where electrons are localized near symmetry centers. Interestingly, localization dependence n n-fold symmetry. Furthermore, macroscopically degenerate zero energy present due chiral rhombic tilings. case, each level forms an independent island trapped at given fields, but control, interference between islands gives rise abrupt change local density states. Our work provide general scheme understand electron behavior