  Using density functional electronic structure calculations, we establish the
consequences of surface termination and modification on protected
surface-states of metacinnabar (beta-HgS). Whereas we find that the Dirac cone
is isotropic and well-separated from the valence band for the (110) surface, it
is highly anisotropic at the pure (001) surface. We demonstrate that the
anisotropy is modified by surface passivation because the topological
surface-states include contributions from dangling bonds. Such dangling bonds
exist on all pure surfaces within the whole class HgX with X = S, Se, or Te and
directly affect the properties of the Dirac cone. Surface modifications also
alter the spatial location (depth and decay length) of the topologically
protected edge-states which renders them essential for the interpretation of
photoemission data.
