Effects of Metallic Contacts on Electron Transport through Graphene

We report on a first-principles study of the conductance through graphene suspended between Al contacts as a function of junction length, width, and orientation. The charge transfer at the leads and into the freestanding section gives rise to an electron-hole asymmetry in the conductance and in sufficiently long junctions induces two conductance minima at the energies of the Dirac points for suspended and clamped regions, respectively. We obtain the potential profile along a junction caused by doping and provide parameters for effective model calculations of the junction conductance with weakly interacting metallic leads.

Figure 1

(a) Band structure and (b) density of states (DOS) for graphene near the Dirac point ($E_D=0$). The two van Hove singularities are marked. (c) Conductance of a graphene ribbon 98.1 nm wide without metallic leads. Inset: The resistance $R$ diverges at the Dirac point. Dashed lines in (b) and (c) are results of tight-binding calculations. (d) Band structure and (e) projected DOS on carbon atoms for graphene on Al. The highlighted lines in (d) are graphene bands.

Figure 2

(a) Schematics of Al-graphene junctions. The semi-infinite leads, shown in the shaded regions, include both graphene and Al. The edges of the ribbon are either armchair ($\mathbf{1}$) or zigzag (${\mathbf{1}}^{\prime }$). The unit cell sizes along the $x$ direction are $w_0=0.49\mathrm{nm}$ and $w_0^{\prime }=0.85\mathrm{nm}$, respectively. $L$ is the distance between Al atoms at opposite sides of the junction. (b) Energy location of the Dirac point with respect to the Fermi level across the junctions. Junctions $\mathbf{1}$, $\mathbf{2}$, and $\mathbf{3}$ have a fixed width $W=98.1\mathrm{nm}$, and lengths $L=3.40$, 6.80, and 13.60 nm, respectively. The DFT results (dots) are shown along with fitted curves (see text).

Figure 3

(a) Conductance of junctions with a width of $W=98.1\mathrm{nm}$ and different lengths $L$. The curves are offset by $20\times 2e^2/h$ for clarity. Two prominent conductance minima at $E_D$ ($-0.6\mathrm{eV}$) and $E_F$ (set to zero) develop as $L$ increases. The symbols represent first-principles results, and the solid lines are from model calculations (see text). Inset: Minimum conductance versus $L$ (the dashed line is a guide to the eye). (b) Conductance of junctions with a length of $L=3.4\mathrm{nm}$ and different widths $W$, highlighting the opening of a conduction gap as $W$ decreases and a sharp peak pinned at $E_D=-0.6\mathrm{eV}$.

Figure 4

(a) Conductance for junctions $\mathbf{1}$ (armchair edges, $L=3.40\mathrm{nm}$, $W=98.1\mathrm{nm}$, dark dots) and ${\mathbf{1}}^{\prime }$ (zigzag edges, $L=3.44\mathrm{nm}$, $W=98.6\mathrm{nm}$, light line). (b) Conductance for junctions consisting of graphene with Au leads for two values of $L$ from model calculations (see text). The junction width is $W=98.1\mathrm{nm}$.