Abstract
We focus on the damping of the lowest-lying gapped modes with integer angular-momentum quantum number in carbon nanotubes (CNTs). These modes, called C modes simply, can be predicted within the framework of the continuum elasticity theory with the curvature term. Based on the phonon-phonon interactions due to the anharmonic effect, we obtain the three-phonon coupling coefficients of different damping processes of C modes. Applying perturbation theory, we calculate relaxation rates and upper bounds of quality factors for the long-wavelength C modes. In addition, we display the wave vector dependence of and show the importance of the C mode damping to thermal conductivity.
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