Symmetry properties of impurities in metallic single-wall carbon nanotubes

Edward McCann, Vladimir I. Fal'ko

    Research output: Contribution to journalArticlepeer-review


    We use the effective mass model to describe spinless electrons near the Fermi level in metallic, single-wall carbon nanotubes. Taking into account two nonequivalent valleys (K-points) produces a four component Dirac equation for massless fermions, with the role of spin assumed by pseudospin due to the relative amplitude of the wavefunction on the two nonequivalent sublattice atoms. We show that the position of a short-ranged impurity within the hexagonal graphite unit cell produces a particular 4 x 4 matrix structure of the corresponding effective Hamiltonian. The symmetry of this Hamiltonian with respect to pseudospin flip is related to degeneracy breaking and, for an armchair tube, symmetry with respect to mirror reflection in the nanotube axis is related to pseudospin mixing. In a nanotube of finite length, we predict a sinusoidal oscillation of energy level shift as a function of energy with a period determined by the position of the impurity along the tube axis.

    Original languageEnglish
    Pages (from-to)3195-3212
    Number of pages18
    JournalInternational Journal of Modern Physics B
    Issue number23-24
    Publication statusPublished - 10 Oct 2004


    • Carbon nanotubes
    • Effective-mass theory
    • Impurity
    • Intervalley scattering
    • Quantum dots

    Research Beacons, Institutes and Platforms

    • National Graphene Institute


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