Lattice thermal conductivity of single-walled carbon nanotubes: Beyond the relaxation time approximation and phonon-phonon scattering selection rules

We present a theoretical description of phonon thermal transport and intrinsic lattice thermal conductivity in single-walled carbon nanotubes (SWCNTs). An exact solution of the phonon Boltzmann equation is implemented using an efficient scheme that allows consideration of SWCNTs with a wide range of radii and chiralities. Our approach combines for the first time calculations of the full spectrum of anharmonic three-phonon scattering processes in SWCNTs with use of the correct selection rules that severely restrict the phase space of this scattering. In particular, we demonstrate that if only the acoustic phonon branches are considered, no umklapp scattering can occur: scattering of acoustic phonons by optic phonons is required to produce thermal resistance in SWCNTs. We also show that the commonly used relaxation time approximation gives a particularly poor description of thermal transport in SWCNTs because of the unusually weak phonon-phonon umklapp scattering in these systems.