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Durham University

Department of Mathematical Sciences


Publication details for Bernard Piette

Brizhik, L., Eremko, A., Piette, B. & Zakrzewski, W.J. (2009), Davydov's solitons in zigzag carbon nanotubes, International Journal of Quantum Chemistry 110: Molecular Self-Organization in Micro-, Nano-, and Macro-Dimensions: From Molecules to Water, to Nanoparticles, DNA and Proteins. Wiley, 11-24.

Author(s) from Durham


Nonlinear mechanism of charge transport in low-dimensional nanosystems is considered, based on the account of the electron–phonon interaction that arises from the deformation dependencies of the on-site and the hopping interaction energies at intermediatevalues of the corresponding coupling constants. In particular, carbon-type hexagonal zigzag nanotubes are studied. It is shown that in the adiabatic approximation the electron–phonon coupling results in the self-trapping of carriers and formation of polaron (soliton) states. We show that the ground state of an electron in a nanotube is a low-dimensional polaron whose symmetry depends on the strength of the coupling. Namely, at relatively weak coupling, the polaron possesses quasi-one-dimensional properties and has an azimuthal symmetry. When the coupling constant exceeds some critical value, the azimuthal symmetry breaks down and two-dimensional polaron on the nanotube surface is formed. There are also polarons formed by the electrons in the conducting band (or by holes in the valence band) in semiconducting zigzag carbon nanotubes. Such polarons are described by the system of coupled nonlinear Schroedinger equations which admits single-band polarons, and entangled (hybridized) polarons. These two types of polarons possess different energies and symmetry properties. Single-band solutions are one-dimensional polarons: they are azimuthally symmetric and localized along the nanotube axis. The entangled polarons are also self-trapped along the nanotube axis, but possess an inner structure and are modulated around the nanotube. The entangled polarons break the azimuthal symmetry and their energy is lower than the energy of single-band polarons. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010