  Topological insulators (TIs) are said to be stable against non-magnetic
impurity scattering due to suppressed backscattering in the Dirac surface
states. We solve a lattice model of a three-dimensional TI in the presence of
strong potential impurities and find that both the Dirac point and low-energy
states are significantly modified: low-energy impurity resonances are formed
that produce a peak in the density of states near the Dirac point, which is
destroyed and split into two nodes that move off-center. The impurity-induced
states penetrate up to 10 layers into the bulk of the TI. These findings
demonstrate the importance of bulk states for the stability of TIs and how they
can destroy the topological protection of the surface.
