  We study the conductance of an interconnect between two graphene leads formed
by a single-atom carbon chain. Its dependence on the chemical potential and the
number of atoms in the chain is qualitatively different from that in the case
of normal metal leads. Electron transport proceeds via narrow resonant states
in the wire. The latter arise due to strong reflection at the junctions between
the chain and the leads, which is caused by the small density of states in the
leads at low energy. The energy dependence of the transmission coefficient near
resonance is asymmetric and acquires a universal form at small energies. We
find that in the case of leads with the zigzag edges the dispersion of the edge
states has a significant effect on the device conductance.
