  The characterization and applications of topological insulators depend
critically on their protected surface states, which, however, can be obscured
by the presence of trivial dangling bond states. Our first principle
calculations show that this is the case for the pristine $(111)$ surface of
SnTe. Yet, the predicted surface states unfold when the dangling bond states
are passivated in proper chemisorption. We further extract the anisotropic
Fermi velocities, penetration lengths and anisotropic spin textures of the
unfolded $\bar\Gamma$- and $\bar M$-surface states, which are consistent with
the theory in http://dx.doi.org/10.1103/PhysRevB.86.081303 Phys. Rev. B 86,
081303 (R). More importantly, this chemisorption scheme provides an external
control of the relative energies of different Dirac nodes, which is
particularly desirable in multi-valley transport.
