2008/11/11 by А. В. Николаев, A. V. Nikolaev, A. V. Bibikov +6
Materials Science · Physics and Astronomy · #Carbon Nanotubes in Composites #Graphene research and applications #Quantum and electron transport phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.79.045418
6 pages, 5 figures
arxiv created 2008/11/11 · openalex publication_date 2009/01/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study one-dimensional (1D) carbon ribbons with the armchair edges and the zigzag carbon nanotubes and their counterparts with finite length [zero dimension (0D)] in the framework of the H"uckel model. Using boundary conditions we derive energy spectra for 1D carbon ribbons. At the Fermi level we construct the explicit solutions and prove the rule of metallicity. We show that the dispersion law (electron band energy) of a 1D metallic ribbon or a 1D metallic carbon nanotube has a universal sinelike dependence at the Fermi energy which is independent of its width. We find that in case of metallic graphene ribbons of finite length (rectangular graphene macromolecules) or nanotubes of finite length the discrete energy spectrum in the vicinity of \ensuremathε=0 (Fermi energy) can be obtained exactly by selecting levels from the same dispersion law. In case of a semiconducting graphene macromolecule or a semiconducting nanotube of finite length, the positions of energy levels around the energy gap can be approximated with a good accuracy. The electron spectrum of 0D carbon structures often includes additional states at energy \ensuremathε=0, which are localized on zigzag edges and do not contribute to the volume conductivity.