Nanotube heat conductors under tensile strain: Reducing the three-phonon scattering strength of acoustic phonons

Acoustic phonons play a special role in lattice heat transport, and confining these low-energy modes in low-dimensional materials may enable nontrivial transport phenomena. By applying lowest-order anharmonic perturbation theory to an atomistic model of a carbon nanotube, we investigate numerically and analytically the spectrum of three-phonon scattering channels in which at least one phonon is of low energy. Our calculations show that acoustic longitudinal (LA), flexural (FA), and twisting (TW) modes in nanotubes exhibit a distinct dissipative behavior in the long-wavelength limit, $|k|\ensuremath{\rightarrow}0$, which manifests itself in scattering rates that scale as ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LA}}\ensuremath{\sim}{|k|}^{\ensuremath{-}1/2}, {\mathrm{\ensuremath{\Gamma}}}_{\mathrm{FA}}\ensuremath{\sim}{k}⁰$, and ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{TW}}\ensuremath{\sim}{|k|}^1/2$. These scaling relations are a consequence of the harmonic lattice approximation and critically depend on the condition that tubes are free of mechanical strain. In this regard, we show that small amounts of tensile lattice strain $\ensuremath{\epsilon}$ reduce the strength of anharmonic scattering, resulting in strain-modulated rates that, in the long-wavelength limit, obey $\mathrm{\ensuremath{\Gamma}}\ensuremath{\sim}{\ensuremath{\epsilon}}^r{|k|}^s$ with $r\ensuremath{\le}0$ and $s\ensuremath{\ge}1$, irrespectively of acoustic mode polarization. Under the single-mode relaxation time approximation of the linearized Peierls-Boltzmann equation (PBE), the long-tube limit of lattice thermal conductivity in stress-free and stretched tube configurations can be unambiguously characterized. Going beyond relaxation time approximations, analytical results obtained in the present study may help to benchmark numerical routines which aim at deriving the thermal conductivity of nanotubes from an exact solution of the PBE.