Disorder-induced pseudodiffusive transport in graphene nanoribbons

We study the transition from ballistic to diffusive and localized transport in graphene nanoribbons in the presence of binary disorder, which can be generated by chemical adsorbates or substitutional doping. We show that the interplay between the induced average doping (arising from the nonzero average of the disorder) and impurity scattering modifies the traditional picture of phase-coherent transport. Close to the Dirac point, intrinsic evanescent modes produced by the impurities dominate transport at short lengths giving rise to a regime analogous to pseudodiffusive transport in clean graphene, but without the requirement of heavily doped contacts. This intrinsic pseudodiffusive regime precedes the traditional ballistic, diffusive, and localized regimes. The last two regimes exhibit a strongly modified effective number of propagating modes and a mean free path which becomes anomalously large close to the Dirac point.

Figure 1

(Color online) Schematic view of an armchair ribbon with width $W$. Disorder is introduced in a region of length $L$ by adding a potential $V_0$ to a percentage $p$ of lattice sites. Disorder sites are depicted by dots. The induced local doping, due to the nonzero average of the disorder, is effectively described by a barrier of height $\overline{V}=p{V}_0$.

Figure 2

(Color online) Averaged conductance $⟨G⟩$ (in units $G_0=\frac{2e^2}{h}$) of an armchair ribbon of width $W=103\sqrt{3}a/2$ as a function of the length of the disordered region for different chemical potentials. The parameters of the binary disorder are $p=0.4$, $V_0=0.25t$, so that the effective Dirac point in the disordered region is shifted from zero to $\overline{V}=p{V}_0=0.1t$. Dashed curves are fits to Eq. (3), with $l_m$ as a fit parameter. Inset: pseudodiffusive regime zoom in. Thin gray curves correspond to different disorder realizations. Good agreement is obtained with the ballistic conductance through a square potential barrier of height $\overline{V}$, shown in dashed black, see Eq. (2).

Figure 3

(Color online) Conductivity $\sigma =⟨G⟩L/W$ versus length for an armchair ribbon of width $W=103\sqrt{3}a/2$ at the effective Dirac point $\mu =\overline{V}$ and fixed impurity fraction $p=0.4$. Different curves correspond to different strength $V_0=\overline{V}/p$ of the disorder. As the chemical potential of the effective Dirac point increases, the number $N$ of incoming modes grows, and a plateau develops at the universal conductivity minimum $2G_0/\pi$ (dashed black line).

Figure 4

(Color online) Mean free path as a function of chemical potential for a metallic armchair nanoribbon of width $W=103\sqrt{3}a/2$, impurity strength $V_0=0.25t$, and impurity fraction $p=0.4$. Black curve: bulk value, Eq. (4). Light (red) curve: finite width result, Eq. (5). Dots: values obtained by fitting numerical results to Eq. (3).

Figure 5

(Color online) Conductance of a graphene armchair ribbon of length $L=3000a$ and width $W=103\sqrt{3}a/2$ for different values of the impurity fraction $p$ and scattering potential $V_0$. The chemical potential is fixed to $\mu =0.1t$. The solid line corresponds to the condition $\mu =\overline{V}=p{V}_0$. The dotted lines are guides for the eyes, bounding the region of increased conductance around the effective Dirac energy.