Charge Transport in Graphene with Resonant Scatterers

The full counting statistics for the charge transport through an undoped graphene sheet in the presence of strong potential impurities is studied. Treating the scattering off the impurity in the $s$-wave approximation, we calculate the impurity correction to the cumulant generating function. This correction is universal provided the impurity strength is tuned to a resonant value. In particular, the conductance of the sample acquires a correction of $16e^2/({\pi }^{2}h)$ per resonant impurity.

Figure 1

Ballistic graphene setup with various strong scatterers. Vacancies as well as atomic or molecular impurities can create midgap states [15]. Metallic islands support quasibound states that can be tuned to the resonance.

Figure 2

Contribution to the conductance $G$ (solid line) and to the shot noise $S$ (dashed line) from a resonant impurity placed at $x_0=L/2$, as a function of the aspect ratio $W/L$. Dotted lines show asymptotic values from Eq. (1). Inset: conductance and noise of a clean sample, cf. Ref. 5.

Figure 3

Correction to the conductance from a circular impurity at $x_0=L/2$ as a function of $u_{0}a$. Solid line: analytic result, Eqs. (7, 10); dotted line: numerical simulations [26] with the parameters $a/L=0.2$, $W/L=6$.

Figure 4

Conductance vs $L$ for resonant impurities. Dotted lines: (a) one- and (b) two-impurity contributions. Inset: corresponding typical diagrams. Dashed line illustrates schematically the crossover to diffusive regime.