The transport properties of the atomic scale side contact between different metals (Au, Ag, Pt, Cu, Ni, Pd) and graphene with open zigzag ends have been studied from first-principles electron transport calculations. According to the contact configurations, we find the weakly interacting metals (Au, Ag, Pt and Cu) can form chemical bonds at the open graphene's atomic edges, while the strongly interacting ones form chemical bonds in the whole contact region. Comparing with the case of end contact which could effectively decrease the contact resistance, the atomic scale side contact shows better transport properties than the end contact. And the graphene/metal side contact with hydrogen terminated graphene edge show obviously large resistance than the ones with open graphene edge, which signifies the importance of the termination of graphene edge in graphene/metal contact.
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