Phonon-phonon interactions and phonon damping for the curvature modes in carbon nanotubes

We focus on the damping of the lowest-lying gapped modes with integer angular-momentum quantum number vertical bar l vertical bar = 2 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 tau(-1)(C) C and upper bounds of quality factors for the long-wavelength C modes. In addition, we display the wave vector dependence of tau(C) and show the importance of the C mode damping to thermal conductivity. Copyright (C) EPLA, 2016