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Degeneracy breaking and intervalley scattering due to short-ranged impurities in finite single-wall carbon nanotubes.

McCann, Edward and Fal’ko, Vladimir I. (2005) Degeneracy breaking and intervalley scattering due to short-ranged impurities in finite single-wall carbon nanotubes. Physical Review B, 71 (8). 085415. ISSN 1550-235X

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    Abstract

    We present a theoretical study of degeneracy breaking due to short-ranged impurities in finite, single-wall, metallic carbon nanotubes. The effective mass model is used to describe the slowly varying spatial envelope wavefunctions of spinless electrons near the Fermi level at two inequivalent valleys (K-points) in terms of the four component Dirac equation for massless fermions, with the role of spin assumed by pseudospin due to the relative amplitude of the wave function on the sublattice atoms (“A” and “B”). Using boundary conditions at the ends of the tube that neither break valley degeneracy nor mix pseudospin eigenvectors, we use degenerate perturbation theory to show that the presence of impurities has two effects. Firstly, the position of the impurity with respect to the spatial variation of the envelope standing waves results in a sinusoidal oscillation of energy level shift as a function of energy. Secondly, the position of the impurity within the hexagonal graphite unit cell produces a particular 4 × 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, the symmetry with respect to mirror reflection in the nanotube axis is related to pseudospin mixing.

    Item Type: Article
    Journal or Publication Title: Physical Review B
    Additional Information: © 2005 The American Physical Society
    Subjects: Q Science > QC Physics
    Departments: Faculty of Science and Technology > Physics
    ID Code: 30829
    Deposited By: Dr Edward McCann
    Deposited On: 08 Dec 2009 11:44
    Refereed?: Yes
    Published?: Published
    Last Modified: 26 Jul 2012 16:50
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/30829

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