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

¹ Key Laboratory of Modern Acoustics and Department of Physics, Nanjing University - Nanjing 210093, China
² Joint Center of Nuclear Science and Technology, Nanjing University - Nanjing 210093, China
³ Center of Theoretical Nuclear Physics, National Laboratory of Heavy-Ion Accelerator - Lanzhou 730000, China

^(a) li.guolong@outlook.com
^(b) zren@nju.edu.cn

Received: 14 September 2015
Accepted: 10 January 2016

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.