Edge state effects in junctions with graphene electrodes

We consider plane junctions with graphene electrodes, which are formed by a single-level system (“molecule”) placed between the edges of two single-layer graphene half planes. We calculate the edge Green functions of the electrodes and the corresponding lead self-energies for the molecular levels in the cases of semi-infinite single-layer electrodes with armchair and zigzag edges. We show two main effects: first, a peculiar energy-dependent level broadening, reflecting at low energies the linear energy dependence of the bulk density of states in graphene, and, second, the shift and splitting of the molecular level energy, especially pronounced in the case of the zigzag edges due to the influence of the edge states. These effects give rise to peculiar conductance features at finite bias and gate voltages.

Figure 1

(top) Example of a plane graphene molecular junction and (bottom) its schematic representation of the considered single-level model for a zigzag edge.

Figure 2

Edge Green function $G_{nn}\left(\epsilon \right)$ for the armchair edge.

Figure 3

Edge Green function $G_{nn}\left(\epsilon \right)$ for the zigzag edge with (a) only nearest-neighbor hopping $t$ and (b) additional next-nearest-neighbor hopping $t^{\prime }=0.1t$.

Figure 4

Spectral function of a single level coupled to armchair edges. The equidistant dashed lines show the position of the level in the wideband limit with $V_0=0.1t$.

Figure 5

Spectral function of a single level coupled to zigzag edges. The dashed lines show the position of the levels in the wideband limit with $V_0=0.1t$.

Figure 6

Color-coded strength of the spectral function of a single level coupled to (a) wideband leads, (b) armchair leads, and (c) zigzag leads. The scale of the spectral function is shown at the right.

Figure 7

Differential conductance $dI/dV$ as a function of bias and gate voltage for a single level at ${\epsilon }_0=0$ coupled to (a) wideband leads, (b) armchair leads, and (c) zigzag leads, with $V_0=0.1t$ and $k_{B}T=0.01t$. The scale of the differential conductance is shown at the right.

Figure 8

The energy level diagrams corresponding to points (a)–(d) marked in Fig. 7c for the differential conductance for zigzag electrodes. The vertical axis corresponds to the energies. The linear energy dependence of the bulk density of states near the Dirac point is shown schematically for the left and right leads (the singular edge-state density of states at the Dirac point is not shown). See the text for explanations.