Flat band has attracted more and more interest in recent years, motivated by its
discovery in twisted bilayer graphene (TBG). In this work, we report our study of the impurity
effect on this flat band system, which is an important issue for real materials. Employing
the Lanczos recursive method, we solve the local density of states (LDOS) around a potential
impurity. We find for large impurity size, a series of bound states are formed inside the
impurity, and the flat band peak in LDOS is suppressed near the impurity boundary and
shifted by the impurity potential deep inside the impurity. As the impurity size becomes
smaller, the effect on the flat band becomes weaker, as anticipated from the large scale of
the underlying Wannier function. This property distinguishes with the usual flat band systems
with small localized Wannier orbitals, and indicates the flat band in TBG is more stable against
small-size impurities.
