Journal of Physics and Chemistry of Solids 69 (2008) 1162–1164 Peculiar electronic transport properties of disordered nanographene ribbons Katsunori Wakabayashi à Department of Quantum Matter, AdSM, Hiroshima University, Higashi-Hiroshima 739-8530, Japan Received 16 June 2007; received in revised form 15 September 2007; accepted 30 October 2007 Abstract The band structure of graphene ribbons with zigzag edges have two valleys well separated in momentum space, related to the two Dirac points of the graphene spectrum. The propagating modes in each valley contain a single chiral mode originating from a partially flat band at band center. This feature gives rise to a perfectly conducting channel in the disordered system, if the impurity scattering does not connect the two valleys, i.e. for long-range impurity potentials. Ribbons with short-range impurity potentials, however, through inter-valley scattering display ordinary localization behavior. r 2007 Elsevier Ltd. All rights reserved. Keywords: A. Semiconductors; C. Ab initio calculations; D. Transport properties The recent fabrication of graphene devices and the observation of half-integer quantum Hall effect [1] have triggered the intensive research on graphenes. Due to the two-dimensional honeycomb structure, the itinerant p-electrons near the Fermi energy behave as massless Dirac fermion. In graphene, the presence of edges can have strong implications for the spectrum of the p-electrons [2]. There are two basic shapes of edges, armchair and zigzag which determine the properties of graphene ribbons. In ribbons with zigzag edges, localized states appear at the edge with energies close to the Fermi level [2]. In contrast, edge states are absent for ribbons with armchair edges. Recent experiments give evidence for edge localized states [3]. The electron transport in one-dimensional (1D) carbon systems displays unusual properties, in apparent conflict with the common belief that 1D systems are generally subjected to Anderson localization. Indeed it was demon- strated that carbon nanotubes with long-ranged impurities (LRI) possess one perfectly conducting channel (PCC) [4]. In this paper, we focus on disorder effects of the electronic transport properties of graphene zigzag ribbons. The edge states play an important role here, since they appear as special modes with partially flat bands and lead under certain conditions to chiral modes. There is one such mode of opposite orientation in each of the two valleys, which are well separated in k-space. The key result of this study is that for disorder without inter-valley scattering a single PCC emerges associated with such a chiral mode. This mode disappears as soon as inter-valley scattering is possible. This distinction depends on the range of the impurity potentials. We describe the electronic states of nanographites by the tight-binding model H ¼ X i;j g i;j jiihj jþ X i V i jiihij, (1) where g i;j ¼1 if i and j are nearest neighbors, and 0 otherwise. jii represents the state of the p z -orbital on site i neglecting the spin degrees of freedom. The second term in Eq. (1) represents the impurity potential, V i ¼ V ðr i Þ is the impurity potential at a position r i . As shown in Fig. 1(a), our zigzag ribbons are character- ized by the width N, the number of zigzag chains, and L denotes the length of the disordered region. In Fig. 1(b), we display the band structure for the zigzag ribbon with N ¼ 10. Note that zigzag ribbons are metallic for all widths at finite doping because of the presence of a partial flat ARTICLE IN PRESS www.elsevier.com/locate/jpcs 0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2007.10.100 à Tel.: +81 82 424 7654; fax: +81 82 424 7000. E-mail address: kwaka@hiroshima-u.ac.jp