Phonon-phonon interactions and phonon damping in carbon nanotubes

TL;DR

This paper develops a quantum theory for acoustic phonons in carbon nanotubes, deriving phonon interactions and damping mechanisms, revealing a thermally smeared gap, and providing bounds on phonon quality factors.

Contribution

It presents a comprehensive analytical framework for phonon interactions in nanotubes, including derivation of coupling constants and nonperturbative effects.

Findings

Finite-temperature flexural phonon density diverges, requiring nonperturbative treatment.

A dynamical gap opens in the phonon spectrum, affecting phonon behavior.

Calculated phonon decay rates set upper bounds for their quality factors.

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.