Thermal response functions and second sound in single-layer hexagonal boron nitride

TL;DR

This study uses equilibrium molecular-dynamics simulations to compute thermal-response functions in single-layer hexagonal boron nitride, revealing strong deviations from Fourier's law and identifying conditions under which second sound can be observed. By linking time-dependent heat transport to the underlying phonon band structure, the work shows that second-sound lifetimes are primarily controlled by nonlinear dispersion and interband coherence rather than solely by anharmonic scattering. The authors also outline a first-principles, many-body approach based on the Bethe-Salpeter equation to compute these response functions from fundamental phonon properties, bridging microscopic phonon dynamics with macroscopic heat flow. The findings suggest that second sound is most accessible in simple, linearly dispersive crystals at low temperatures and short length scales, and they provide a framework for predicting heat transport in regimes where Fourier's law fails.

Abstract

Ballistic heat transport and second sound propagation in solids is of direct relevance in electronic and energy applications at short length scales and low temperatures. Measurement or calculation of thermal conductivity, which is typically a primary objective, may be of limited usefulness for predicting heat transport which does not follow the heat-diffusion equation. In this paper, molecular-dynamics simulations of hexagonal BN (h-BN) are used to compute thermal response functions from equilibrium correlation functions defined in Fourier space. The response functions are useful for describing the time-dependent transport beyond the usual assumptions of Fourier's law. The results demonstrate that for length scales ~110nm at T=100K second sound should be experimentally observable. At higher temperatures and longer length scales, while second sound may not be directly observable, thermal transport can nevertheless strongly deviate from predictions based on the heat-diffusion equation. Along with classical simulations, we outline a first-principles, many-body theoretical approach for calculation of the response function based on solutions of the Bethe-Salpeter equation. The relevant expressions for heat current clarify the importance of phase coherence within a phonon branch to the observation of second sound. Previous work on one-dimensional chains is also discussed to show that materials characterized by linear dispersion and simple phonon band structure should more readily display second sound.

Figures (12)

• Figure 1: Thermal conductivity integral in Eq. \ref{['GK']} plotted as a function of the upper integration limit $\tau$ for different equilibration times $\tau_{eq}$. In each instance the system temperature was $T=300$K.
• Figure 2: Response function $K_{\bm{q}}(\tau)$ plotted as a function of response time $\tau$ for $q={2 \pi \over \lambda}$ with $\lambda=6.93$nm. The system temperature was $T=300$K. The oscillatory behavior is characteristic of second sound propagation.
• Figure 3: Response function $K^{\prime \prime}_{\bm{q}}(\omega)$ plotted as a function of frequency ${\omega \over 2 \pi}$. Results obtained for $T=300$K and $q={2 \pi \over \lambda}$ with $\lambda=6.93$nm. The response based on the heat-diffusion equation is also shown (solid green line).
• Figure 4: Real part of the response function $K^{\prime}_{\bm{q}}(\omega)$ plotted as a function of frequency ${\omega \over 2 \pi}$. Results obtained for $T=300$K and $q={2 \pi \over \lambda}$ with $\lambda=6.93$nm. The response based on the heat-diffusion equation is also shown (solid green line).
• Figure 5: Response function $K^{\prime \prime}_{\bm{q}}(\omega)$ plotted as a function of frequency ${\omega \over 2 \pi}$. Results obtained for $T=300$K and $q={2 \pi \over \lambda}$ with $\lambda=6.93$nm. The response based on the heat-diffusion equation is also shown (solid green line).