  We investigate the effect of a non-magnetic donor impurity located at the
surface of the SnTe topological crystalline insulator. In particular, the
changes on the surface states due to a Sb impurity atom are analyzed by means
of ab initio simulations of pristine and impurity-doped SnTe. Both
semi-infinite and slab geometries are considered within the first-principles
approach. Furthermore, minimal and Green's function continuum models are
proposed with the same goal. We find that the Dirac cones are shifted down in
energy upon doping; this shift strongly depends on the position of the impurity
with respect to the surface. In addition, we observe that the width of the
impurity band presents an even-odd behavior by varying the position of the
impurity. This behavior is related to the position of the nodes of the wave
function with respect to the surface, and hence it is a manifestation of
confinement effects. We compare slab and semi-infinite geometries within the ab
initio approach, demonstrating that the surface states remain gapless and their
spin textures are unaltered in the doped semi-infinite system. In the slab
geometry, a gap opens due to hybridization of the states localized at opposite
surfaces. Finally, by means of a continuum model, we extrapolate our results to
arbitrary positions of the impurity, clearly showing a non-monotonic behavior
of the Dirac cone.
