Phonon-phonon interactions and phonon damping in carbon nanotubes

Abstract

We formulate and study the effective low-energy quantum theory of interacting long-wavelength acoustic phonons in carbon nanotubes within the framework of continuum elasticity theory. A general and analytical derivation of all three- and four-phonon processes is provided, and the relevant coupling constants are determined in terms of few elastic coefficients. Due to the low dimensionality and the parabolic dispersion, the finite-temperature density of noninteracting flexural phonons diverges, and a nonperturbative approach to their interactions is necessary. Within a mean-field description, we find that a dynamical gap opens. In practice, this gap is thermally smeared, but still has important consequences. Using our theory, we compute the decay rates of acoustic phonons due to phonon-phonon and electron-phonon interactions, implying upper bounds for their quality factor.

15 pages, 2 figures, published version

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• Interrelation of elasticity and thermal bath in nanotube cantilevers
• Material limitations of carbon-nanotube inertial balances: on the possibility of intrinsic yoctogram mass resolution at room temperature
• Theory of phonon-drag thermopower of extrinsic semiconducting single-wall carbon nanotubes and comparison with previous experimental data
• Damping of mechanical vibrations by free electrons in metallic nanoresonators
• Vibron-vibron coupling from ab initio molecular dynamics simulations of a silicon cluster
• Nanotube heat conductors under tensile strain: Reducing the three-phonon scattering strength of acoustic phonons
• Theory of the conductance of interacting quantum wires with good contacts and applications to carbon nanotubes