  The contact conductance between graphene and two quantum wires which serve as
the leads to connect graphene and electron reservoirs is theoretically studied.
Our investigation indicates that the contact conductance depends sensitively on
the graphene-lead coupling configuration. When each quantum wire couples solely
to one carbon atom, the contact conductance vanishes at the Dirac point if the
two carbon atoms coupling to the two leads belong to the same sublattice of
graphene. We find that such a feature arises from the chirality of the Dirac
electron in graphene. Such a chirality associated with conductance zero
disappears when a quantum wire couples to multiple carbon atoms. The general
result irrelevant to the coupling configuration is that the contact conductance
decays rapidly with the increase of the distance between the two leads. In
addition, in the weak graphene-lead coupling limit, when the distance between
the two leads is much larger than the size of the graphene-lead contact areas
and the incident electron energy is close to the Dirac point, the contact
conductance is proportional to the square of the product of the two
graphene-lead contact areas, and inversely proportional to the square of the
distance between the two leads.
