Two-dimensional graphene, carbon nanotubes, and graphene nanoribbons represent a novel class of low dimensional materials that could serve as building blocks for future carbon-based nanoelectronics. Although these systems share a similar underlying electronic structure, whose exact details depend on confi nement effects, crucial differences emerge when disorder comes into play. In this review, we consider the transport properties of these materials, with particular emphasis on the case of graphene nanoribbons. After summarizing the electronic and transport properties of defect-free systems, we focus on the effects of a model disorder potential (Anderson-type), and illustrate how transport properties are sensitive to the underlying symmetry. We provide analytical expressions for the elastic mean free path of carbon nanotubes and graphene nanoribbons, and discuss the onset of weak and strong localization regimes, which are genuinely dependent on the transport dimensionality. We also consider the effects of edge disorder and roughness for graphene nanoribbons in relation to their armchair or zigzag orientation.

We provide a general procedure for the description and evaluation of the current distribution in mesoscopic quantum wires. Our approach is based on the Keldysh-Green function formalism of nonequilibrium quantum statistical mechanics and exploits the real-space renormalization method within the tight-binding framework. We obtain a detailed spatial description of the microscopic currents between any couple of sites of the system, both in the presence and in the absence of time-reversal symmetry. As an application we present current profiles for a disordered quantum wire in the regime of universal conductance fluctuations, and we illustrate the random path of the current flow also in the presence of a magnetic field

The role of defect-induced zero-energy modes on charge transport in graphene is investigated using Kubo and Landauer transport calculations. By tuning the density of random distributions of monovacancies either equally populating the two sublattices or exclusively located on a single sublattice, all conduction regimes are covered from direct tunneling through evanescent modes to mesoscopic transport in bulk disordered graphene. Depending on the transport measurement geometry, defect density, and broken sublattice-symmetry, the Dirac point conductivity is either exceptionally robust against disorder (supermetallic state) or suppressed through a gap opening or by algebraic localization of zero-energy modes, whereas weak localization and the Anderson insulating regime are obtained for higher energies. These findings clarify the contribution of zero-energy modes to transport at the Dirac point, hitherto controversial.The electronic transport properties of graphene are known to be very peculiar with unprecedented manifestations of quantum phenomena such as Klein tunneling [1, 2], weak antilocalization [3,4], or the anomalous quantum Hall effect [5,6], all driven by a π-Berry phase stemming from graphene sublattice symmetry and pseudospin degree of freedom [7][8][9]. These fascinating properties, yielding high charge mobility [10,11], are robust as long as disorder preserves a long range character. The fundamental nature of transport precisely at the Dirac point is, however, currently a subject of fierce debate and controversies. Indeed, for graphene deposited on oxide substrates, the nature of low-energy transport physics (as its sensitivity to weak disorder) is masked by the formation of electron-hole puddles [9]. A remarkable experiment has, however, recently demonstrated the possibility to screen out these detrimental effects [12], providing access to the zero-energy Dirac physics. An unexpectedly large increase of the resistivity at the Dirac point was tentatively related to the Anderson localization [12,13] of an unknown physical origin and questioned interpretation [14].Of paramount importance are therefore the low-energy impurity states known as zero-energy modes (ZEMs) [15,16], whose impact on the Dirac-point transport physics needs to be clarified. ZEMs are predicted or observed for a variety of disorder classes, as topological defects (mainly vacancies) [16,17], adatoms covalently bonded to carbon atoms [18,19], and extended defects as grain boundaries [20,21]. As recently confirmed by scanning tunneling microscopy experiments on graphene monovacancies [22], ZEMs manifest as wave functions that decay as the inverse of the distance from the vacancy, exhibiting a puzzling quasilocalized character, whose consequences on quantum transport remain, to date, highly controversial. First, ZEMs have been predicted to produce a supermetallic regime by enhancing the Dirac-point conductivity above its minimum ballistic value σ min = 4e 2 /πh [23,24], an unprecedented conducting state, which could be, in principle, explo...

We present first-principles transport calculations of graphene nanoribbons with chemically reconstructed edge profiles. Depending on the geometry of the defect and the degree of hydrogenation, spectacularly different transport mechanisms are obtained. In the case of monohydrogenated pentagon (heptagon) defects, an effective acceptor (donor) character results in strong electron-hole conductance asymmetry. In contrast, weak backscattering is obtained for defects that preserve the benzenoid structure of graphene. Based on a tight-binding model derived from ab initio calculations, evidence for large conductance scaling fluctuations are found in disordered ribbons with lengths up to the micrometer scale.

The electronic structure and the current profiles of n - and p -doped graphene ribbons are investigated within the Keldysh Green’s function method in the tight-binding framework. The low energy spectrum, at the heart of the relativisticlike quantum transport, is studied numerically and relevant features are understood analytically by means of the continued fraction tool. Simulations of charge transport and spatial distribution of spectral currents in field-effect controlled graphene ribbons are then carried out in the absence and in the presence of uniform magnetic fields. The role of gated regions and threading magnetic fields for manipulating the flow of Dirac particles is investigated

We report a theoretical low-field magnetotransport study unveiling the effect of pseudospin in realistic models of weakly disordered graphene-based materials. Using an efficient Kubo computational method, and simulating the effect of charges trapped in the oxide, different magnetoconductance fingerprints are numerically obtained in system sizes as large as 0.3µm 2 , containing tens of millions of carbon atoms. In two-dimensional graphene, a strong valley mixing is found to irreparably yield a positive magnetoconductance (weak localization), whereas crossovers from positive to a negative magnetoconductance (weak antilocalization) are obtained by reducing disorder strength down to the ballistic limit. In sharp contrast, graphene nanoribbons with lateral size as large as 10nm show no sign of weak antilocalization, even for very small disorder strength. Our results rationalize the emergence of a complex phase diagram of magnetoconductance fingerprints, shedding some new light on the microscopical origin of pseudospin effects.In 2004, the report on graphene discovery [1] has sparked a great scientific excitement because of both novel type of electronic excitations (so-called massless Dirac Fermions) [2] and a promising future of graphene-based technologies [3]. In two-dimensional graphene, the very peculiar nature of low-energy electronic states (encompassing a new pseudospin degree of freedom) yields a wealth of anomalous transport features such as Klein tunneling [4], weak antilocalization [5,6], unconventional quantum Hall effect [7,8], or new ways (supercollimation) to guide charge flows [9] .Besides, the nature of disorder, its effect on electronic properties, and the envisionned defect engineering for novel graphene electronics are currently subjects of great concern [10, 11]. However to date, the precise relationship between the underlying disorder features and the onset of graphene unique transport properties remains debated. The question also applies to graphene nanoribbons which exhibit different electronic properties induced by p-1

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We report on (magneto)-transport experiments in chemically derived narrow graphene nanoribbons under high magnetic fields (up to 60 Tesla). Evidences of field-dependent electronic confinement features are given, and allow estimating the possible ribbon edge symmetry. Besides, the measured large positive magnetoconductance indicates a strong suppression of backscattering induced by the magnetic field. Such scenario is supported by quantum simulations which consider different types of underlying disorders (smooth edge disorder and long range Coulomb scatters).