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Symmetry properties of impurities in metallic single-wall carbon nanotubes.

Research output: Contribution to journalJournal article

Published

Journal publication date10/10/2004
JournalInternational Journal of Modern Physics B
Journal number23-24
Volume18
Number of pages18
Pages3195-3212
Original languageEnglish

Abstract

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 4×4 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.