Signatures of coherent phonon transport in frequency dependent lattice thermal conductivity

TL;DR

This work introduces the frequency-dependent lattice thermal conductivity, $κ(ν)$, as a direct probe of coherent phonon transport, separating particle-like and coherent contributions within the Green–Kubo framework. It shows that coherent transport produces non-monotonic spectral peaks when driving frequency matches mode-frequency differences for the same wave vector, a feature absent in purely particle-like transport. Applying the theory to CuCl reveals clear sub-THz coherent signatures and peaks at a few THz, highlighting the importance of mode nesting and higher-order anharmonic effects. The study also discusses experimental challenges for detecting $κ(ν)$ and proposes pathways, including exploration in amorphous or disordered materials and potential connections to topological phonon states, with significant implications for high-frequency thermal management and material design.

Abstract

Thermal transport in highly anharmonic, amorphous, or alloyed materials often deviates from the predictions of conventional phonon-based models. First-principles approaches have introduced a coherent contribution to account for these deviations and to explain ultra-low lattice thermal conductivity, but direct experimental evidence for this mechanism remains elusive. Here, we propose that the frequency-dependent lattice thermal conductivity, $κ(ν)$, provides a direct signature of coherent transport. Specifically, we show that peaks in $κ(ν)$ arise from the frequency nesting of modes with identical wave vectors. Applying this approach to CuCl, we identify clear signatures of coherent transport in its dynamical lattice thermal conductivity. We revisit the interpretation of thermoreflectance experiments and argue that the conventional understanding breaks down in strongly anharmonic crystals, alloys, and amorphous materials. Finally, we discuss experimental pathways to measure $κ(ν)$, offering a new route to verify coherent contributions in thermal transport.

Figures (6)

• Figure 1: Calculated and measured phonon band structure of CuCl. The full black lines are SSCHA calculations, while experiments are shown in points (red CuCl_phonons_exp and blue CuClkappa_theory1). Dashed lines represent phonon density of states calculated using phonon spectral functions. Shaded regions represent phonon frequency nesting responsible for spectral signatures in Fig. \ref{['fig:ls']}.
• Figure 1: Left: Temperature dependent phonon dispersion of CuCl. Right: Lattice thermal conducitivity of CuCl calculated with 0 K force constants (black line) and temperature dependent force constants (black stars) compared with experiment (red circles).
• Figure 2: Calculated and measured lattice thermal conductivity $\kappa$ of CuCl. The full black line is total $\kappa$, dashed line is the diagonal contribution and pointed line is the off-diagonal, coherent, contribution. Experiment CuCl_kappa is shown in red points. The inset shows the phonon mean free path at 300 K with dashed line being the lattice constant indicating boundary for diffusive transport.
• Figure 2: Dynamical lattice thermal conductivity of AgI, AlAs, AlN and BN at 300 K. Solid lines are calculations done using Supp. Eq. \ref{['diag_pert']} and \ref{['pert_nondiag']}. Blue crosses are results for cumulative lattice thermal conductivity with mean free path converted to driving frequency $\nu = \frac{\kappa (L_p)}{\pi C L_p ^2}$. Green circles is total lattice thermal conductivity but with maximum phonon mean free path set to $L_p$. Force constants for these materials are taken form PhononDB database CuCl_kappa_theory2.
• Figure 3: Dynamical lattice thermal conductivity. (a) Total dynamical lattice thermal conductivity at different temperatures. (b) Dynamical lattice thermal conductivity at 450 K. The black cross denotes the frequency at which coherent transport gives dominant contribution. The green crosses are results for the mean free path cumulative lattice thermal conductivity expressed in appropriate frequency.