  Based on first-principles calculations we predict a peculiar growth process,
where carbon adatoms adsorbed to graphene readily diffuse above room
temperature and nucleate segments of linear carbon chains attached to graphene.
These chains grow longer on graphene through insertion of carbon atoms one at a
time from the bottom end and display a self-assembling behavior. Eventually,
two allotropes of carbon, namely graphene and cumulene are combined to exhibit
important functionalities. The segments of carbon chains on graphene become
chemically active sites to bind foreign atoms or large molecules. When bound to
the ends of carbon chains, transition metal atoms, Ti, Co and Au, attribute a
magnetic ground state to graphene sheets and mediate stable contacts with
interconnects. We showed that carbon chains can grow also on single wall carbon
nanotubes.
