Electron transport from a one-dimensional lead to a two-dimensional graphene sheet through a single site

The problem of electron transport through a graphene-based device is studied theoretically and numerically. The device is composed of a single central site, with a single energy level, which is connected to a one-dimensional lead, and a two-dimensional graphene sheet. The nonequilibrium Green function formalism is utilized in modeling the problem; the formulation and numerical calculations are carried out around a K-point, in the band structure of the graphene, where the Fermi energy is located. Particular importance is placed on the transmission and current–voltage (I–V) characteristics of the device under a small bias. We find that the graphene part causes the central transmission peak, originally due to the single energy level of the central site, to split into two peaks, leaving an anti-resonant, zero-transmission, dip between them; only one of these peaks contributes to the resultant current. There always appears an almost flat, practically zero-current, region on a rather large bias interval, centered around the Fermi energy of the graphene, in the I–V graphs.