  Silicene and germanene derivatives constructed from periodic dumbbell units
play a crucial role in multilayers of these honeycomb structures. Using
first-principles calculations based on density functional theory, here we
investigate the dumbbell formation mechanisms and energetics of Group IV atoms
adsorbed on graphene, silicene, germanene and stanene monolayer honeycomb
structures. The stabilities of the binding structures are further confirmed by
performing ab-initio molecular dynamics calculations at elevated temperatures,
except for stanene which is subject to structural instability upon the
adsorption of adatoms. Depending on the row number of the adatoms and
substrates we find three types of binding structures, which lead to significant
changes in the electronic, magnetic, and optical properties of substrates. In
particular, Si, Ge and Sn adatoms adsorbed on silicene and germanene form
dumbbell structures. Furthermore, dumbbell structures occur not only on single
layer, monatomic honeycomb structures, but also on their compounds like SiC and
SiGe. We show that the energy barrier to the migration of a dumbbell structure
is low due to the concerted action of atoms. This renders dumbbells rather
mobile on substrates to construct new single and multilayer Si and Ge phases.
