Nonlinear Transport Through Ultra Narrow Zigzag Graphene Naoribbons

Abstract

Graphene, a monolayer of a honeycomb lattice of carbon atoms has been attracted a great amount of attention from both experimental and theoretical points of view Novoselov et al. (2006). Flat structure of graphene makes its fabrication more straightforward than carbon nanotubes. Moreover, dreams of carbon nanoelectronic approach to the reality based on planar graphene structures. This structure overcomes some difficulties of nanoelectronics based on carbon nanotubes, by using lithography, one-dimensional ribbon patterns on graphene sheets Liu et al. (2009). Experiments in graphene-based devices Ozyilmaz et al. (2007) have shown the possibility of controlling their electrical properties by the application of an external gate voltage. For achieving realistic nanoelectronic applications based on graphene nanoribbons (GNR), width of ribbon have to be narrow enough that a transport gap is opened Han el al. (2007); Li et al. (2008); Wang et al. (2008). Using a chemical process, sub-10 nm GNR field-effect-transistors with very smooth edges have been obtained in Ref.[ Li et al. (2008); Wang et al. (2008)] and demonstrated to be semiconductors with band-gap inversely proportional to the width and on/off ratio of current up to 106 at room temperature. By connecting GNRs with different types of edges and widths, it is applicable to fabricate electronic devices based on graphene nanoribbons. The origin of transport gap which is opened in a gate voltage region of suppressed nonlinear conductance is still not well understood Molitor et al. (2009); Son et al. (2006); Sols et al. (2007). Two factors are responsible for transport gap: the edge disorder leading to localization Mucciolo et al. (2009) and the confinement Nakada et al. (1996); Brey & Fertig-a (2006); BeryF Zheng et al. (2007); Malysheva& Onipko (2008). However, in nonlinear regime, transport gap is also opened by transition selection rules which originates from the reflection symmetry Duan et al. (2008). Based on the tight-binding approach, GNRs with armchair shaped edges are either metal or Semiconductor Son et al. (2006); Nakada et al. (1996); Brey & Fertig-a (2006); BeryF Zheng et al. (2007). Moreover, in this approach, zigzag edge ribbons are metal regardless of their widths Malysheva& Onipko (2008). While ab initio calculations Son et al. (2006) predict that regardless of the shape of the edges, GNRs are semiconductor. In zigzag GNRs, the bands are partially flat around the Fermi energy, which means that the group velocity of conduction electrons is close to zero. Their transport properties are dominated by edge states. Similar to carbon nanotubes, electronic transition through a ZGNRs follows from some selection rules. The rotational symmetry of the incoming electron wave function with respect 7