Impurity-assisted tunneling in graphene

The electric conductance of a strip of undoped graphene increases in the presence of a disorder potential, which is smooth on atomic scales. The phenomenon is attributed to impurityassisted resonant tunneling of massless Dirac fermions. Employing the transfer matrix approach we demonstrate the resonant character of the conductivity enhancement in the presence of a single impurity. We also calculate the two-terminal conductivity for the model with one-dimensional fluctuations of disorder potential by a mapping onto a problem of Anderson localization. A monoatomic layer of graphite, or graphene, has been recently proven to exist in nature [1–4]. Low-energy excitations in graphene are described by the ”relativistic” massless Dirac equation, which gives us theoretical insight into exotic transport properties observed in this material. Undoped graphene is a gapless semiconductor, or semimetal, with vanishing density of states at the Fermi level. One of the first experiments [2] shows that the conductivity of graphene at low temperatures takes on a nearly universal value of the order of 4e/h and increases if a doping potential of any polarity is applied. Systematic dependence of the minimal conductivity on the sample size has been observed recently in Ref. [17]. The peculiar band-structure of the two-dimensional carbon, which mainly explains many recent experimental observations, has already been calculated in 1947 by Wallace [5]. Nevertheless, the universal value of the minimal conductivity is not entirely understood. Many recent theoretical studies [8–13] address the problem of the finite conductivity of the undoped graphene by employing the Kubo formula. Other works [14–16] show that the conductance G of a ballistic graphene sample (of the width W much larger than the length L) scales as G = σW/L with the coefficient σ = 4e/πh. This value of σ coincides with the prediction made for the dc conductivity of disordered graphene [6–9, 12, 13] and agrees with experiments done on small samples [17]. In this work we develop an extension of the transfer matrix formalism of Refs. [16, 18, 19] in order to include the effects of disorder. Our main result is the enhancement of the zero temperature conductance at low dopkx q