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Quantum-mechanical calculations of electron transport in ideal graphene nanoribbons show that the transport gap that is predicted by noninteracting theories vanishes if the long-range Coulomb interaction between electrons is taken into account. This is a result of charge screening with the lowest subband edge being pinned to the chemical potential. However, the transport gap reappears if a ribbon is connected to wider leads, which is typically realized in an experimental setup that is based on lithographically patterned graphene ribbons. The gap is determined by scattering at the lead-to-ribbon interface, which can already be captured by the noninteracting theory. [ABSTRACT FROM AUTHOR]

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 Hückel 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. [ABSTRACT FROM AUTHOR]

We provide a systematic quantitative description of spin polarization in armchair and zigzag graphene nanoribbons (GNRs) in a perpendicular magnetic field. We first address spinless electrons within the Hartree approximation, studying the evolution of the magnetoband structure and formation of the compressible strips. We discuss the potential profile and the density distribution near the edges and the difference and similarities between armchair and zigzag edges. Accounting for the Zeeman interaction and describing the spin effects via the Hubbard term, we study the spin-resolved subband structure and relate the spin polarization of the system at hand to the formation of the compressible strips for the case of spinless electrons. At high magnetic field the calculated effective g factor varies around a value of 〈g*〉 ≈ 2.25 for armchair GNRs and 〈g*&#12297 ≈ 3 for zigzag GNRs. An important finding is that in zigzag GNRs the zero-energy mode remains pinned to the Fermi energy and becomes fully spin polarized for all magnetic fields, which, in turn, leads to a strong spin polarization of the electron density near the zigzag edge. Because of this the effective g factor in zigzag GNRs is strongly enhanced at low fields reaching values up to g* ≈ 30. This is in contrast to armchair GNRs, where the effective g factor at low field is close to its bare value, g = 2. [ABSTRACT FROM AUTHOR]

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 x 2e2/h as in recent experiments [N. Tombros et al, Nat. Phys. 7, 697 (2011)]. We demonstrate that, surprisingly, conductances quantized in integer multiples of 2e2/ h occur even for strongly nonadiabatic 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 x 2e2/ h can occur as a result of electron backscattering at stepped edges even in the absence of electron-electron interactions. [ABSTRACT FROM AUTHOR]

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 the following. (i) Electrons accumulating along the edges of the uniform ribbon and along the 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 intrasubband scattering while the noninteracting electron theory predicts the predominance of intersubband 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 2e²/h conductance plateau for the cosine constriction than is found in the absence of electron interactions. Possible implications for recent experiments are briefly discussed. [ABSTRACT FROM AUTHOR]