Average density of states in disordered graphene systems

In this paper, the average density of states (ADOS) in graphene with binary alloy disorders is calculated by the recursion method. We observed an obvious resonant peak and a dip in ADOS curves near the Dirac point, which result from interactions with surrounding impurities. We also found that the resonance energy $\left(E_r\right)$ and the dip position $\left({\epsilon }_{\text{dip}}\right)$ are strongly dependent on the concentration of disorders $\left(x\right)$ and their on-site potentials $\left(v\right)$. A linear relation, ${\epsilon }_{\text{dip}}=xv$, holds when the impurity concentration is low. This relation can also be extended when the impurity concentration is high, but with certain constraints. We also compute ADOS with a finite density of vacancies.

Figure 1

(Color online) The honeycomb lattice of a graphene. Here, a unit cell is outlined by the red dashed lines, and two nonequivalent atoms are labeled with A (green sphere) and B (blue sphere), respectively.

Figure 2

(Color online) (a) $\epsilon$ and (b) DOS as a function of $L$ (blue solid line) and the corresponding fitting line shown with a red dashed line for a perfect graphene. Insets in (a) and (b) indicate that the relations $\epsilon \sim 1/L$ and $\rho \sim 1/L$ approximately hold at the Dirac point. (c) DOS $\left(\rho \right)$ as a function of $N$ (blue solid line) at the Dirac point $\left(E=0\right)$. Here, $L=800$.

Figure 3

(Color online) [(a) and (b)] ADOS of a graphene with impurity concentration $x=10\%$ and various on-site potentials $\left(v\right)$. (c) The energy shift of the antiresonance state $\left({\epsilon }_{\text{dip}}\right)$ as a function of the on-site potential $\left(v\right)$ (blue solid line). The red dashed line stands for the linear relation ${\epsilon }_{\text{dip}}=xv$. (d) The resonance energy $\left(E_r\right)$ as a function of the on-site potential $\left(v\right)$. The blue, green, and red lines stand for the ADOS of a graphene with $x=10\%$. ADOS is calculated by using the recursion method. LDOS of a single impurity is computed by using the recursion method and EMA.

Figure 4

(Color online) (a) ADOS of a disordered graphene and (b) ADOS near the Dirac point with various impurity concentrations $\left(x\right)$. Here, $v=1.5$. (c) The energy shift $\left({\epsilon }_{\text{dip}}\right)$ as a function of impurity concentrations $\left(x\right)$ (blue solid line) for $v=1.5$. The red dashed line shows the following linear relation: ${\epsilon }_{\text{dip}}=xv$.

Figure 5

(Color online) (a) Parameter $\kappa v$ and (b) the energy shift $\left({\epsilon }_{\text{dip}}\right)$ as a function of on-site potential $\left(v\right)$, where the impurity concentration is $x=10\%$. The blue and red solid lines stand for the results calculated by using the recursion method and the CPA, respectively. The green dashed line indicates the linear relation ${\epsilon }_{\text{dip}}=xv$.

Figure 6

(Color online) (a) Parameter $\kappa v$ and (b) the energy shift $\left({\epsilon }_{\text{dip}}\right)$ as a function of impurity concentration $\left(x\right)$ when $v=1.5$ (blue line) or $v=5$ (dark cyan lines). The red solid line indicates $\kappa$ as a function of impurity concentration for the $v=1.5$ case. The green dashed line shows the linear relation of ${\epsilon }_{\text{dip}}=xv$.

Figure 7

(Color online) (a) ADOS of a disordered graphene and (b) ADOS near the Dirac point with various impurity concentrations $\left(x\right)$. Here, $v=5$.

Figure 8

(Color online) The calculated ADOS of graphene with different concentrations of vacancies. Here, we choose $v=1000$.