Theoretical study of thermal conductivity in single-walled boron nitride nanotubes

We perform a theoretical investigation on the thermal conductivity of single-walled boron nitride nanotubes (SWBNT) using the kinetic theory. By fitting to the phonon spectrum of the boron nitride sheet, we develop an efficient and stable Tersoff-derived interatomic potential which is suitable for the study of heat transport in sp2 structures. We work out the selection rules for the three-phonon process with the help of the helical quantum numbers (kappa,n) attributed to the symmetry group (line group) of the SWBNT. Our calculation shows that the thermal conductivity kappa(ph) diverges with length as kappa(ph) alpha L-beta with exponentially decaying beta(T) alpha e(-T/Tc), which results from the competition between boundary scattering and three-phonon scattering for flexure modes. We find that the two flexure modes of the SWBNT make dominant contribution to the thermal conductivity, because their zero frequency locates at kappa = +/-alpha, where alpha is the rotational angle of the screw symmetry in SWBNT.