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

TL;DR

This paper uses molecular dynamics and theoretical approaches to analyze thermal response functions and second sound in hexagonal boron nitride, revealing conditions for observing second sound and deviations from Fourier's law at nanoscale and low temperatures.

Contribution

It introduces a method to compute thermal response functions from equilibrium correlations in h-BN and discusses the conditions for second sound observation, advancing understanding of non-diffusive heat transport.

Findings

Second sound observable at ~110nm and 100K in h-BN.

Thermal transport deviates from Fourier's law at larger scales and higher temperatures.

Phase coherence within phonon branches is crucial for second sound detection.

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.