A theoretical study of thermal conductivity in single-walled boron nitride nanotubes

Abstract

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 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 ${\kappa }_{\mathrm{ph}}$ diverges with length as ${\kappa }_{\mathrm{ph}}\propto L^{\beta }$ with exponentially decaying $\beta (T)\propto e^{-T/T_c}$, 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 $\kappa =\pm \alpha$ where $\alpha$ is the rotational angle of the screw symmetry in SWBNT.

accepted by PRB

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