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A 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 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 $(κ, n)$ attributed to the symmetry group (line group) of the SWBNT. Our calculation shows that the thermal conductivity $κ_{\rm ph}$ diverges with length as $κ_{\rm ph}\propto L^β$ with exponentially decaying $β(T)\propto e^{-T/T_{c}}$, 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 $κ=\pmα$ where $α$ is the rotational angle of the screw symmetry in SWBNT.