Color-Dependent Conductance of Graphene with Adatoms

We study ballistic transport properties of graphene with a low concentration of vacancies or adatoms. The conductance of graphene doped to the Dirac point is found to depend on the relative distribution of impurities among different sites of the honeycomb lattice labeled in general by six colors. The conductivity is shown to be sensitive to the crystal orientation if adatom sites have a preferred color. Our theory is confirmed by numerical simulations using recursive Green’s functions with no adjustable parameters.

Figure 1

Color scheme for vacancies or resonant adatoms. The impurity site is characterized by the phase ${\theta }_{\pm }^c=\pm \alpha +2\pi c/3$, where $\pm$ refers to the sublattice ($A$ or $B$) and $c=-1,0,1$ denotes the colors (red, green, and blue, respectively). The color scheme depends on the transport direction $x$. The phases at $A$ and $B$ sites connected by the vector ${\mathbf{\delta }}_0$ are equal for $\alpha =0$, while they differ most for $\alpha =\pi /6$.

Figure 2

Conductance variation for an armchair ($\alpha =0$) sample with two vacancies ($A$ and $B$). On changing the distance $\overline{y}$, the conductance jumps on the atomic scale between three different smooth curves corresponding to $\overline{\theta }=0$ (green disks), $\overline{\theta }=2\pi /3$ (blue squares), and $\overline{\theta }=-2\pi /3$ (red diamonds). The numerical data agree well with Eq. (10), as shown by the corresponding curves.

Figure 3

Conductance variation for a zigzag ($\alpha =\pi /6$) sample with two vacancies. Top panel: $A$ and $B$ vacancies. On changing $\overline{y}$, the conductance jumps on the atomic scale between different smooth curves corresponding to $\overline{\theta }=\pi$ (green disks), $\pi /3$ (blue squares), and $-\pi /3$ (red diamonds). Bottom panel: Both vacancies in $A$ sublattice. The phase difference $\overline{\theta }$ is either 0 (green disks), $2\pi /3$ (blue squares), or $-2\pi /3$ (red diamonds). The numerical data agree well with the result Eq. (10), as shown by the corresponding curves.