Phonon-phonon interactions and phonon damping in carbon nanotubes

Details Phonon-phonon interactions and phonon damping in carbon nanotubes Phonon-phonon interactions and phonon damping in carbon nanotubes

2009-03-10

arxiv.org/abs/0903.1771v2

Phys. Rev. B 79, 205408 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

15 pages, 2 figures, published version

Scientific paper

10.1103/PhysRevB.79.205408

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.

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