We study the effect of the edge disorder on the conductance of the graphene nanoribbons (GNRs). We find that only very modest edge disorder is sufficient to induce the conduction energy gap in the otherwise metallic GNRs and to lift any difference in the conductance between nanoribbons of different edge geometry. We relate the formation of the conduction gap to the pronounced edge disorder induced Anderson-type localization which leads to the strongly enhanced density of states at the edges, formation of surface-like states and to blocking of conductive paths through the ribbons.

A theoretical study of the transport properties of zigzag and armchair graphene nanoribbons with a magnetic barrier on top is presented. The magnetic barrier modifies the energy spectrum of the nanoribbons locally, which results in an energy shift of the conductance steps towards higher energies. The magnetic barrier also induces Fabry − Pérot type oscillations, provided the edges of the barrier are sufficiently sharp. The lowest propagating state present in zigzag and metallic armchair nanoribbons prevent confinement of the charge carriers by the magnetic barrier. Disordered edges in nanoribbons tend to localize the lowest propagating state, which get delocalized in the magnetic barrier region. Thus, in sharp contrast to the case of two-dimensional graphene, the charge carriers in graphene nanoribbons cannot be confined by magnetic barriers. We also present a novel method based on the Green's function technique for the calculation of the magnetosubband structure, Bloch states and magnetoconductance of the graphene nanoribbons in a perpendicular magnetic field. Utilization of this method greatly facilitates the conductance calculations, because, in contrast to excising methods, the present method does not require self-consistent calculations for the surface Green's function.

A theoretical study of the magnetoelectronic properties of zigzag and armchair bilayer graphene nanoribbons (BGNs) is presented. Using the recursive Green's function method, we study the band structure of BGNs in uniform perpendicular magnetic fields and discuss the zero-temperature conductance for the corresponding clean systems. The conductance quantized as 2(n + 1)G0 for the zigzag edges and nG0 for the armchair edges with G0 = 2e 2 /h being the conductance unit and n an integer. Special attention is paid to the effects of edge disorder. As in the case of monolayer graphene nanoribbons (GNR), a small degree of edge disorder is already sufficient to induce a transport gap around the neutrality point. We further perform comparative studies of the transport gap Eg and the localization length ξ in bilayer and monolayer nanoribbons. While for the GNRs E GNR g ∼ 1/W , the corresponding transport gap E BGN g for the bilayer ribbons shows a more rapid decrease as the ribbon width W is increased. We also demonstrate that the evolution of localization lengths with the Fermi energy shows two distinct regimes. Inside the transport gap, ξ is essentially independent on energy and the states in the BGNs are significantly less localized than those in the corresponding GNRs. Outside the transport gap ξ grows rapidly as the Fermi energy increases and becomes very similar for BGNs and GNRs.

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We derive analytical expressions for the conductivity of bilayer graphene (BLG) using the Boltzmann approach within the the Born approximation for a model of Gaussian disorders describing both short-and long-range impurity scattering. The range of validity of the Born approximation is established by comparing the analytical results to exact tight-binding numerical calculations. A comparison of the obtained density dependencies of the conductivity with experimental data shows that the BLG samples investigated experimentally so far are in the quantum scattering regime where the Fermi wavelength exceeds the effective impurity range. In this regime both short-and long-range scattering lead to the same linear density dependence of the conductivity. Our calculations imply that bilayer and single-layer graphene have the same scattering mechanisms. We also provide an upper limit for the effective, density-dependent spatial extension of the scatterers present in the experiments.

The effects of electron interaction on the magnetoconductance of graphene nanoribbons (GNRs) are studied within the Hartree approximation. We find that a perpendicular magnetic field leads to a suppression instead of an expected improvement of the quantization. This suppression is traced back to interaction-induced modifications of the band structure leading to the formation of compressible strips in the middle of GNRs. It is also shown that the hard-wall confinement combined with electron interaction generates overlaps between forward and backward propagating states, which may significantly enhance backscattering in realistic GNRs. The relation to available experiments is discussed.Original Publication:Artsem Shylau, Igor Zozoulenko, H Xu and T Heinzel, Generic suppression of conductance quantization of interacting electrons in graphene nanoribbons in a perpendicular magnetic field, 2010, PHYSICAL REVIEW B, (82), 12, 121410.http://dx.doi.org/10.1103/PhysRevB.82.121410Copyright: American Physical Societyhttp://www.aps.org

Ballistic quantum wires are exposed to longitudinal profiles of perpendicular magnetic fields composed of a spike and a homogeneous part. An asymmetric magnetoconductance peak as a function of the homogeneous magnetic field is found, comprising quantized conductance steps in the interval where the homogeneous magnetic field and the magnetic barrier have identical polarities, and a characteristic shoulder with several resonances in the interval of opposite polarities. The observations are interpreted in terms of inhomogeneous diamagnetic shifts of the quantum wire modes leading to magnetic confinement.

The effects of Coulomb interactions on the electronic properties of bilayer graphene nanoribbons ͑BGNs͒ covered by a gate electrode are studied theoretically. The electron-density distribution and the potential profile are calculated self-consistently within the Hartree approximation. A comparison to their single-particle counterparts reveals the effects of interactions and screening. Due to the finite width of the nanoribbon in combination with electronic repulsion, the gate-induced electrons tend to accumulate along the BGN edges where the potential assumes a sharp triangular shape. This has a profound effect on the energy gap between electron and hole bands, which depends nonmonotonously on the gate voltage and collapses at intermediate electric fields. We interpret this behavior in terms of interaction-induced warping of the energy dispersion.