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

TL;DR

This paper presents a theoretical study of thermal conductivity in single-walled boron nitride nanotubes, revealing how it diverges with length and the dominant role of flexure modes, using a new interatomic potential and symmetry analysis.

Contribution

It introduces a Tersoff-derived interatomic potential for heat transport in sp2 structures and analyzes phonon processes using symmetry-based selection rules.

Findings

Thermal conductivity diverges with length as a power law.

Flexure modes dominate thermal transport in SWBNT.

Thermal conductivity depends exponentially on temperature.

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 $\kappa_{\rm ph}$ diverges with length as $\kappa_{\rm ph}\propto L^{\beta}$ 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.