We study numerically the effects of edge and bulk disorder on the conductance of graphene nanoribbons. We compute the conductance suppression due to Anderson localization induced by edge scattering and find that even for weak edge roughness, conductance steps are suppressed and transport gaps are induced. These gaps are approximately inversely proportional to the nanoribbon width. On/off conductance ratios grow exponentially with the nanoribbon length. Our results impose severe limitations to the use of graphene in ballistic nanowires.

We show that a coherent picture of the dc conductivity of monolayer and bilayer graphene at finite electronic densities emerges upon considering that strong short-range potentials are the main source of scattering in these two systems. The origin of the strong short-range potentials may lie in adsorbed hydrocarbons at the surface of graphene. The equivalence among results based on the partial-wave description of scattering, the Lippmann-Schwinger equation, and the T matrix approach is established. Scattering due to resonant impurities close to the neutrality point is investigated via a numerical computation of the Kubo formula using a kernel polynomial method. We find that relevant adsorbate species originate impurity bands in monolayer and bilayer graphene close to the Dirac point. In the midgap region, a plateau of minimum conductivity of about e 2 /h (per layer) is induced by the resonant disorder. In bilayer graphene, a large adsorbate concentration can develop an energy gap between midgap and high-energy states. As a consequence, the conductivity plateau is supressed near the edges and a "conductivity gap" takes place. Finally, a scattering formalism for electrons in biased bilayer graphene, taking into account the degeneracy of the spectrum, is developed and the dc conductivity of that system is studied.

We describe how to apply the recursive Green's function method to the computation of electronic transport properties of graphene sheets and nanoribbons in the linear response regime. This method allows for an amenable inclusion of several disorder mechanisms at the microscopic level, as well as inhomogeneous gating, finite temperature, and, to some extend, dephasing. We present algorithms for computing the conductance, density of states, and current densities for armchair and zigzag atomic edge alignments. Several numerical results are presented to illustrate the usefulness of the method.

We propose a mechanism by which an open quantum dot driven by two ac (radio frequency) gate voltages in the presence of a moderate in-plane magnetic field generates a spin-polarized, phase-coherent dc current. The idea combines adiabatic, nonquantized (but coherent) pumping through periodically modulated external parameters and the strong fluctuations of the electron wave function existent in chaotic cavities. We estimate that the spin polarization of the current can be observed for temperatures and Zeeman splitting energies of the order of the single-particle mean level spacing.

Abstract. In this review, we provide an account of the recent progress in understanding electronic transport in disordered graphene systems. Starting from a theoretical description that emphasizes the role played by band structure properties and lattice symmetries, we describe the nature of disorder in these systems and its relation to transport properties. While the focus is primarily on theoretical and conceptual aspects, connections to experiments are also included. Issues such as short versus long-range disorder, localization (strong and weak), the carrier density dependence of the conductivity, and conductance fluctuations are considered and some open problems are pointed out.

Using the recursive Green's function method, we study the problem of electron transport in a disordered single-layer graphene sheet. The conductivity is of order e 2 /h and its dependence on the carrier density has a scaling form that is controlled solely by the disorder strength and the ratio between the sample size and the correlation length of the disorder potential. The shot noise Fano factor is shown to be nearly density independent for sufficiently strong disorder, with a narrow structure appearing at the neutrality point only for weakly disordered samples. Our results are in good agreement with experiments and provide a way for extracting microscopic information about the magnitude of extrinsic disorder in graphene.PACS numbers: 81.05. Uw, Graphene, a two-dimensional (2D) allotrope of carbon with a honeycomb lattice, has attracted a lot of attention due to its unusual, Dirac-like, electronic spectrum and its potential for an all-carbon based electronics.1 While the theoretical literature on graphene is already quite extensive, 2 the effect of disorder on transport properties near the charge neutrality point (Dirac point) is still subject to much debate and controversy. The difficulty in understanding how disorder affects Dirac fermions has to do with the fact that electrochemical disorder is a relevant perturbation under the renormalization group and drives the system away from the weak disorder regime.3 Hence, standard perturbation theory fails and one has to rely on either non-perturbative methods or numerical approaches. Although several recent theoretical works have been established that for short-range disorder large graphene samples should become insulators, 4 the current understanding of long-range disorder is less clear. Some authors 5 have questioned the existence of a beta function for undoped graphene while others 6 have proposed a non-monotonic beta function for single-valley Dirac fermions and a metal-insulator transition. Numerical computations in momentum space 7 as well as simulations based on a transfer-matrix method 8,9 adapted to the single-valley Dirac equation 10 found instead a simple scaling law for the conductivity, a metallic beta function, and no indication of a new fixed point.11 Furthermore, while the selfconsistent Born approximation (SCBA) predicts a universal (impurity independent) conductivity of 4e 2 /(πh), 12 percolation theory finds a smaller value. 13On the experimental side, graphene behaves as a good metal with conductivities of the order of e 2 /h, 14 which is inconsistent with a purely ballistic transport. No sign of strong localization has been seen in graphene although the size of the samples (a few micrometers) may be smaller than the localization length in 2D.Current experiments indicate that transport is not ballistic, but is it really diffusive? Experimentally, the electron mean free path ℓ tr can be estimated by gating graphene away from the Dirac point and using the Drude formula to relate ℓ tr to the conductivity σ:where n is the carrier density. Typically,...

Graphene subjected to chiral-symmetric disorder is believed to host zero energy modes (ZEMs) resilient to localization, as suggested by the renormalization group analysis of the underlying nonlinear sigma model. We report accurate quantum transport calculations in honeycomb lattices with in excess of 10 9 sites and fine meV resolutions. The Kubo dc conductivity of ZEMs induced by vacancy defects (chiral BDI class) is found to match 4e 2 =πh within 1% accuracy, over a parametrically wide window of energy level broadenings and vacancy concentrations. Our results disclose an unprecedentedly robust metallic regime in graphene, providing strong evidence that the early field-theoretical picture for the BDI class is valid well beyond its controlled weak-coupling regime.

Abstract. We propose an accurate tight-binding parametrization for the band structure of MoS 2 monolayers near the main energy gap. We introduce a generic and straightforward derivation for the band energies equations that could be employed for other monolayer dichalcogenides. A parametrization that includes spin-orbit coupling is also provided. The proposed set of model parameters reproduce both the correct orbital compositions and location of valence and conductance band in comparison with ab initio calculations. The model gives a suitable starting point for realistic large-scale atomistic electronic transport calculations.