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 combine ab initio density functional theory with transport calculations to provide a microscopic basis for distinguishing between good and poor metal contacts to nanotubes. Comparing Ti and Pd as examples of different contact metals, we trace back the observed superiority of Pd to the nature of the metal-nanotube hybridization. Based on large scale Landauer transport calculations, we suggest that the optimum metal-nanotube contact combines a weak hybridization with a large contact length between the metal and the nanotube. DOI: 10.1103/PhysRevLett.96.076802 PACS numbers: 73.23.Ad, 73.40.Cg, 73.63.Fg, 73.63.Rt A major challenge linked to the use of carbon nanotubes [1] in future electronic devices is to understand the profound effect of the nanotube-metal contact on transport. Weak nanotube-metal coupling, found in nanotubes deposited on metal electrodes, has been shown to cause Coulomb blockade behavior [2]. In spite of significant progress in maximizing the contact area by depositing metal on top of nanotubes [3], the transparency of such contacts exhibits strong sample-to-sample variations and depends strongly on the contact metal. Reports of low contact resistance between nanotubes and Au or Au=Cr [4,5] are in stark contrast to the high resistance observed in nanotube contacts with Au=Ti [6]. The transparency of Pd-based contacts has been reported as superior in comparison to using Ti, Pt, and Al as contact metals [7][8][9]. Additional modulation of the Pd-nanotube contact transparency has been reportedly achieved by modulating the gate voltage [10]. Reports suggesting that carrier injection occurs only at the edge of the contact region [8] appear to contradict the observed dependence of the contact resistance on the length of the contact [6].Published theoretical results include studies of the electronic structure at a nanotube-Au interface and transport properties of a nanotube-Al junction [11]. Ab initio calculations furthermore suggest that Ti contacts may be superior to those with Al or Au [12], and that the Schottky barrier between semiconducting tubes and Pd is lower than with Au or Pt [13]. Because of the limitation to specific contact geometries and small system dimensions, however, general trends are hard to extract, and an extrapolation to experimentally relevant system sizes is difficult.Here we combine ab initio electronic structure studies with large scale transport calculations to gain microscopic insight into the relative importance of the interface morphology, the type of the contact metal, and the length of the contact region when optimizing the metal-nanotube contact. Ab initio density functional studies were used to determine the charge redistribution and electrostatic potential in the contact region. In a second step, the electronic structure results were mapped onto a model tight-binding Hamiltonian suitable for transport calculations. We found that transmission is maximized in the case of weak metalnanotube coupling, exhibited by extended Pd contacts.To gain insight into the elec...

We study the efficiency, precision and accuracy of all-electron variational and diffusion quantum Monte Carlo calculations using Slater basis sets. Starting from wave functions generated by Hartree-Fock and density functional theory, we describe an algorithm to enforce the electron-nucleus cusp condition by linear projection. For the 55 molecules in the G2 set, the diffusion quantum Monte Carlo calculations recovers an average of 95% of the correlation energy and reproduces bond energies to a mean absolute deviation of 3.2 kcal/mol. Comparing the individual total energies with essentially exact values, we investigate the error cancellation in atomization and chemical reaction path energies, giving additional insight into the sizes of nodal surface errors.

Carrier injection into carbon nanotubes and graphene nanoribbons, contacted by a metal coating over an arbitrary length, is studied by various means: Minimal models allow for exact analytic solutions which can be transferred to the original system with high precision. Microscopic ab initio calculations of the electronic structure at the carbon-metal interface allow us to extract-for Ti and Pd as contacting materials-realistic parameters, which are then used in large scale tight-binding models for transport calculations. The results are shown to be robust against nonepitaxially grown electrodes and general disorder at the interface, as well as various refinements of the model.

The electronic spectrum of a two-dimensional square lattice in a perpendicular magnetic field has become known as the Hofstadter butterfly ͓Hofstadter, Phys. Rev. B 14, 2239 ͑1976͒.͔. We have calculated quasi-onedimensional analogs of the Hofstadter butterfly for carbon nanotubes ͑CNTs͒. For the case of single-wall CNTs, it is straightforward to implement magnetic fields parallel to the tube axis by means of zone folding in the graphene reciprocal lattice. We have also studied perpendicular magnetic fields which, in contrast to the parallel case, lead to a much richer, pseudofractal spectrum. Moreover, we have investigated magnetic fields piercing double-wall CNTs and found strong signatures of interwall interaction in the resulting Hofstadter butterfly spectrum, which can be understood with the help of a minimal model. Ubiquitous to all perpendicular magnetic field spectra is the presence of cusp catastrophes at specific values of energy and magnetic field. Resolving the density of states along the tube circumference allows recognition of the snake states already predicted for nonuniform magnetic fields in the two-dimensional electron gas. An analytic model of the magnetic spectrum of electrons on a cylindrical surface is used to explain some of the results.

We calculate the electronic spectrum of bilayer graphene in perpendicular magnetic fields nonperturbatively. To accomodate arbitrary displacements between the two layers, we apply a periodic gauge based on singular flux vortices of phase 2π. The resulting Hofstadter-like butterfly plots show a reduced symmetry, depending on the relative position of the two layers against each other. The split of the zero-energy relativistic Landau level differs by one order of magnitude between Bernal and non-Bernal stacking. After the theoretical prediction of the peculiar electronic properties of graphene in 1947 by Wallace 1 and the subsequent studies of its magnetic spectrum, 2,3 it took half a century until single layers of graphene could be isolated in experiment 4 and the novel mesoscopic properties of these two-dimensional (2D) Dirac-like electronic systems, e.g., their anomalous quantum Hall effect, could be measured. 5,6,7 Inspired by this experimental success, graphene has become the focus of numerous theoretical works. 8,9,10,11,12 For bilayers of graphene, an additional degeneracy of the Landau levels and a Berry phase of 2π were predicted to lead to an anomalous quantum Hall effect, different from either the regular massive electrons or the special Dirac-type electrons of single-layer graphene, 13 which was confirmed in experiment shortly afterwards 14 and used for the characterization of bilayer samples. 15The low-energy electronic structure of a single layer of graphene is well described by a linearization near the corner points of the hexagonal Brillouin zone (K points), resulting in an effective Hamiltonian formally equivalent to that of massless Dirac particles in two dimensions. 16

The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the diffusion Monte Carlo method for large quantum systems. We identify the correlation within the population of walkers as the dominant scaling factor for large systems. While this factor is negligible for small and medium sized systems that are typically studied, it ultimately shows exponential scaling. The scaling factor can be estimated straightforwardly for each specific system and we find that is typically only becomes relevant for systems containing more than several hundred atoms.

We describe a number of strategies for minimizing and calculating accurately the statistical uncertainty in quantum Monte Carlo calculations. We investigate the impact of the sampling algorithm on the efficiency of the variational Monte Carlo method. We then propose a technique to maximize the efficiency of the linear extrapolation of diffusion Monte Carlo results to zero time step, finding that a relative time-step ratio of 1:4 is optimal. Finally, we discuss the removal of serial correlation from data sets by reblocking, setting out criteria for the choice of block length and quantifying the effects of the uncertainty in the estimated correlation length.