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We present numerical studies of conduction in graphene nanoribbons with reconstructed edges based on the standard tight-binding model of the graphene and the extended Huckel model of the reconstructed defects. We performed atomic geometry relaxation of individual defects using density functional theory and then explicitly calculated the tight-binding parameters used to model electron transport in graphene with reconstructed edges. The calculated conductances reveal strong backscattering and electron-hole asymmetry depending on the edge and defect type. This is related to an additional defect-induced band whose wave function is poorly matched to the propagating states of the pristine ribbon. We find a transport gap to open near the Dirac point and to scale inversely with the ribbon width, similarly to what has been observed in experiments. We predict the largest transport gap to occur for armchair edges with Stone-Wales defects, while heptagon and pentagon defects cause about equal backscattering for electrons and holes, respectively. Choosing the heptagon defect as an example, we show that although electron interactions in the Hartree approximation cause accumulation of charge carriers on the defects, surprisingly, their effect on transport is to reduce carrier backscattering by the defects and thus to enhance the conductance., Comment: 8 pages, 4 figures

We present self-consistent calculations of electron transport in graphene nanoconstrictions within the Hartree approximation. We consider suspended armchair ribbons with V-shaped constrictions having perfect armchair or zigzag edges as well as mesoscopically smooth but atomically stepped constrictions with cosine profiles. Our calculations are based on a tight-binding model of the graphene and account for electron-electron interactions in both the constriction and the semi-infinite leads explicitly. We find that electron interactions result in (i) Electrons accumulating along edges of the uniform ribbon and along zigzag and cosine constriction edges but not along armchair constriction edges. (ii) The first subband showing almost perfect transmittance due to localization at the uniform graphene boundary except at low energies for the cases of zigzag and cosine constrictions where Bloch stop-bands form in related periodic structures. (iii) The second subband being almost perfectly blocked by the constriction. (iv) Electron interactions favor intra-subband scattering while the non-interacting electron theory predicts predominance of inter-subband scattering. (v) Conductance quantization for the first few conductance steps being more pronounced for armchair constrictions but less so for zigzag constrictions. (vi) A much more prominent 2e^2/h conductance plateau for the cosine constriction than is found in the absence of electron interactions. Possible implications for recent experiments are briefly discussed., Comment: 8 pages, 7 figures

We present the results of million atom electronic quantum transport calculations for graphene nanoconstrictions with edges that are smooth apart from atomic scale steps. We find conductances quantized in integer multiples of 2e2/h and a plateau at ~0.5*2e2/h as in recent experiments [Tombros et al., Nature Physics 7, 697 (2011)]. We demonstrate that, surprisingly, conductances quantized in integer multiples of 2e2/h occur even for strongly non-adiabatic electron backscattering at the stepped edges that lowers the conductance by one or more conductance quanta below the adiabatic value. We also show that conductance plateaus near 0.5*2e2/h can occur as a result of electron backscattering at stepped edges even in the absence of electron-electron interactions., Comment: 5 pages, 4 figures

We present numerical studies of non-linear conduction in graphene nanoribbons when a bias potential is applied between the source and drain electrodes. We find that the conductance quantization plateaus show asymmetry between the electron and hole branches if the potential in the ribbon equals the source or drain electrode potential and strong electron (hole) scattering occurs. The scattering may be at the ends of a uniform ballistic ribbon connecting wider regions of graphene or may be due to defects in the ribbon. We argue that, in ribbons with strong defect scattering, the ribbon potential is pinned to that of the drain (source) for electron (hole) transport. In this case symmetry between electron and hole transport is restored and our calculations explain the upward shift of the conductance plateaus with increasing bias that was observed experimentally by Lin et al. [Phys. Rev. B 78, 161409 (2008)]., Comment: 6 pages, 3 figures

We present calculations of electronic quantum transport in graphene nanoribbons with adsorbed H, F, OH and O, based on a tight binding model derived from extended Huckel theory. The relaxed atomic geometries of the adsorbates and graphene are calculated using density functional theory. Our model includes the effects of the local rehybridization of the graphene from the sp2 to sp3 electronic structure that occurs when H, F, OH or O bonds covalently to the graphene. It captures the physics of the scattering resonances that are induced in the graphene near the Dirac point by the presence of these adsorbates. We find these Dirac point resonances to play a dominant role in quantum transport in ribbons with these adsorbates: Even at low adsorbate concentrations the conductance of the ribbon is strongly suppressed and a transport gap develops for electron Fermi energies near the resonance. The transport gap is centered very near the Dirac point energy of for H, below it for F and OH and above it for O. We predict ribbons with these adsorbed species under appropriate conditions to exhibit quantized conductance steps of equal height similar to those that have been observed by Lin et al. [Phys. Rev. B 78, 161409 (2008)] at moderately low temperatures, even for ribbons with conductances a few orders of magnitude smaller than 2e2/h., Comment: This paper has been withdrawn by the authors. This paper has been combined with 1008.4110 and published as Phys. Rev. B 83, 245442 (2011)

We present a tight binding theory of the Dirac point resonances due to adsorbed atoms and molecules on an infinite 2D graphene sheet based on the standard tight binding model of the graphene p-band electronic structure and the extended Huckel model of the adsorbate and nearby graphene carbon atoms. The relaxed atomic geometries of the adsorbates and graphene are calculated using density functional theory. Our model includes the effects of the local rehybridization of the graphene from the sp^2 to sp^3 electronic structure that occurs when adsorbed atoms or molecules bond covalently to the graphene. Unlike in previous tight-binding models of Dirac point resonances, adsorbed species with multiple extended molecular orbitals and bonding to more than one graphene carbon atom are treated. More accurate and more general analytic expressions for the Green's function matrix elements that enter the T-matrix theory of Dirac point resonances than have been available previously are obtained. We study H, F, OH and O adsorbates on graphene and for each we find a strong scattering resonance (two resonances for O) near the Dirac point of graphene, by far the strongest and closest to the Dirac point being the resonance for H. We extract a minimal set of tight binding parameters that can be used to model resonant electron scattering and electron transport in graphene and graphene nanostructures with adsorbed H, F, OH and O accurately and efficiently. We also compare our results for the properties of Dirac point resonances due to adsorbates on graphene with those obtained by others using density functional theory-based electronic structure calculations, and discuss their relative merits. We then present calculations of electronic quantum transport in graphene nanoribbons with these adsorbed species..., Comment: 21 pages, 9 figures

We present numerical studies of conduction in graphene nanoribbons with different types of disorder. We find that even when defect scattering depresses the conductance to values two orders of magnitude lower than 2e^2/h, equally spaced conductance plateaus occur at moderately low temperatures due to enhanced electron backscattering near subband edge energies if bulk vacancies are present in the ribbon. This work accounts quantitatively for the surprising conductance quantization observed by Lin et al. [Phys. Rev. B 78, 161409 (2008)] in ribbons with such low conductances., Comment: 4 pages, 3 figures

We calculate the band structure and the conductance of periodic corrugated graphene nanoribbons within the framework of the tight-binding $p$-orbital model. We consider corrugated structures based on host ribbons with armchair and zigzag edges and three different types of corrugations (armchair edges, zigzag edges as well as a rectangular corrugation). We demonstrate that for armchair host ribbons, depending on the type of corrugation, a band gap or low-velocity minibands appear near the charge neutrality point. For higher energies the allowed Bloch state bands become separated by mini-stopbands. By contrast, for corrugated ribbons with the zigzag host, the corrugations introduce neither band gaps nor stopbands (except for the case of the rectangular corrugations). The conductances of finite corrugated ribbons are analyzed on the basis of the corresponding band structures. For a sufficiently large number of corrugations the conductance follows the number of the corresponding propagating Bloch states and shows pronounced oscillations due to the Fabry-Perot interference within the corrugated segments. Finally we demonstrate that edge disorder strongly affects the conductances of corrugated ribbons. Our results indicate that observation of miniband formation in corrugated ribbons would require clean, edge-disorder free samples, especially for the case of the armchair host lattice., Comment: 7 pages, 7 figures

We present a microscopic picture of quantum transport in quantum antidots in the quantum Hall regime taking electron interactions into account. We discuss the edge state structure, energy level evolution, charge quantization and linear-response conductance as the magnetic field or gate voltage is varied. Particular attention is given to the conductance oscillations due to Aharonov-Bohm interference and their unexpected periodicity. To explain the latter we propose the mechanisms of scattering by point defects and Coulomb blockade tunneling. They are supported by self-consistent calculations in the Hartree approximation, which indicate pinning and correlation of the single-particle states at the Fermi energy as well as charge oscillation when antidot-bound states depopulate. We have also found interesting phenomena of anti-resonance reflection of the Fano type., Comment: 12 pages, 8 figures

Coherent quantum transport in ferromagnetic/ semiconductor/ ferromagnetic junctions is studied theoretically within the Landauer framework of ballistic transport. We show that quantum coherence can have unexpected implications for spin injection and that some intuitive spintronic concepts which are founded in semi-classical physics no longer apply: A quantum spin-valve (QSV) effect occurs even in the absence of a net spin polarized current flowing through the device, unlike in the classical regime. The converse effect also arises, i.e. a zero spin-valve signal for a non-vanishing spin-current. We introduce new criteria useful for analyzing quantum and classical spin transport phenomena and the relationships between them. The effects on QSV behavior of spin-dependent electron transmission at the interfaces, interface Schottky barriers, Rashba spin-orbit coupling and temperature, are systematically investigated. While the signature of the QSV is found to be sensitive to temperature, interestingly, that of its converse is not. We argue that the QSV phenomenon can have important implications for the interpretation of spin-injection in quantum spintronic experiments with spin-valve geometries., Comment: 15 pages including 11 figures. To appear in PRB

We have introduced a controllable nano-scale incursion into a potential barrier imposed across a two-dimensional electron gas, and report on the phenomena that we observe as the incursion develops. In the quantum Hall regime, the conductance of this system displays quantized plateaus, broad minima and oscillations. We explain these features and their evolution with electrostatic potential geometry and magnetic field as a progression of current patterns formed by tunneling between edge and localized states within the barrier., Comment: RevTeX + 4 postscript figures. Self-unpacking uuencoded files. Unpacking instructions are at the beginning of the files. To appear in Physical Review B

We present a study of the transport properties of a general class of quantum mechanical waveguides: Quantum Railroads (QRR). These waveguides are characterised by having a different number of adiabatic modes which carry current in one direction along the waveguide to the opposite direction; for example N forward modes and M reverse modes. Just as Anderson localization is a characteristic of the disordered N=M case and the quantum Hall effect a characteristic of the M=0 case we find that a mixed effect, DIRECTED localization, is a characteristic of QRR's. We find that in any QRR there are always |N-M| perfectly transmitted effective adiabatic modes with the remainder being subject to multiple scattering and interference effects characteristic of the N=M case., Comment: revtex 3.0. See Can.J.Phys.72,559(1994) or contact chwb101@cus.cam.ac.uk for figures.