  Surface-states of topological insulators are assumed to be robust against
non-magnetic defects in the crystal. However, recent theoretical models and
experiments indicate that even non-magnetic defects can perturb these states.
Our first-principles calculations demonstrate that the presence of Se vacancies
in Bi$_2$Se$_3$, has a greater impact than a mere n-doping of the structure,
which would just shift the Fermi level relative to the Dirac point. We observe
the emergence of a non-linear band pinned near the Fermi level, while the Dirac
cone shifts deeper into the valence band. We attribute these features in the
bandstructure to the interaction between the surface and defect states, with
the resulting hybridization between these states itself depending on the
position and symmetry of the Se vacancy relative to the surfaces. Our results
bring us a step closer to understanding the exotic physics emerging from
defects in Bi$_2$Se$_3$ that remained unexplored in prior studies.

Materials Science;Mesoscale and Nanoscale Physics