  A new type of long-range ordering in the absence of translational symmetry
gives rise to drastic revolution of our common knowledge in condensed matter
physics. Quasicrystal, as such unconventional system, became a plethora to test
our insights and to find exotic states of matter. In particular, electronic
properties in quasicrystal have gotten lots of attention along with their
experimental realization and controllability in twisted bilayer systems. In
this work, we study how quasicrystalline order in bilayer systems can induce
unique localization of electrons without any extrinsic disorders. We focus on
dodecagonal quasicrystal that has been demonstrated in twisted bilayer graphene
system in recent experiments. In the presence of small gap, we show the
localization generically occurs due to non-periodic nature of quasicrystal,
which is evidenced by the inverse participation ratio and the energy level
statistics. We understand the origin of such localization by approximating the
dodecagonal quasicrystals as an impurity scattering problem.
