  Electrons in graphene with heavy adatoms (such as In or Tl) have been
predicted to form a 2D topological insulator phase with a substantial spectral
gap potentially suitable for future practical applications. In order to
facilitate the ongoing experimental efforts to identify this phase we perform a
theoretical study of its spectral properties in a model graphene system with
randomly distributed adatoms. Our extensive modeling shows that random heavy
adatoms produce a full spectral gap (as opposed to a mobility gap) accompanied
by distinctive quasiparticle interference patterns observable by means of
Fourier-transform scanning tunneling spectroscopy.
