Transition from Population to Coherence-dominated Non-diffusive Thermal Transport

Deviations from diffusive heat transport in high thermal conductivity crystalline insulators are generally understood within the framework of the phonon Boltzmann Transport Equation. However, for low thermal conductivity materials with large primitive cells or strong anharmonicity, the recently developed Wigner Transport Equation is more appropriate as it includes tunnelling between overlapping phonon bands. In this work, via solutions to the Wigner Transport Equation, we develop a scheme to obtain the dynamics of the phonon populations and coherences as a function of an arbitrary heat source. The approach is applied to predict size effects and dynamical thermal conductivities in CsPbBr3 and La2Zr2O7 using first-principles data as input. We predict significant deviations from the bulk thermal conductivity in these materials at length scales on the order of hundreds of nanometers to a few microns at room temperature, well within the reach of direct observation using current experimental techniques.

💡 Research Summary

This paper presents a significant advancement in the theoretical understanding of non-diffusive heat transport in solids, focusing on materials where wave-like phonon tunneling becomes crucial. The authors address a key limitation of the conventional phonon Boltzmann Transport Equation (BTE), which is suitable for high-thermal-conductivity crystals but fails for materials with low thermal conductivity, large primitive cells, or strong anharmonicity. In such materials, phonon linewidths become comparable to the energy spacing between phonon bands, enabling tunneling between overlapping phonon wavefunctions. This necessitates a description that accounts for phonon coherences (off-diagonal elements of the density matrix), not just populations (diagonal elements).

The core of the work is the development and application of a solution scheme for the Wigner Transport Equation (WTE), which naturally includes these coherence effects. The authors generalize the WTE to incorporate an arbitrary space- and time-dependent heat source. By employing Fourier transforms, they recast the problem into a linear system, enabling the calculation of the system’s Green’s function. This framework provides a direct, quantitative link to time-resolved pump-probe experiments, as the Green’s function describes the impulse response of the phonon system.

The theoretical framework is applied to predict thermal transport properties in two low-thermal-conductivity materials, CsPbBr3 and La2Zr2O7, using first-principles input data. The results reveal a fundamental transition in transport mechanism: while in silicon phonon populations dominate entirely, in CsPbBr3 and La2Zr2O7, the contribution from phonon coherences is significant and even becomes the dominant contributor to total thermal conductivity above certain temperatures (e.g., ~240 K for CsPbBr3, ~800 K for La2Zr2O7). This highlights a “coherence-dominated” regime previously inaccessible to BTE-based models.

Furthermore, the paper investigates size effects by calculating the thermal conductivity as a function of thermal grating period (Λ). They predict that in La2Zr2O7, the population contribution (from a few long-mean-free-path acoustic modes) begins to drop at grating periods on the order of 10 micrometers, while the more broadly distributed coherence contribution remains robust until periods shrink to around 50 nanometers. In CsPbBr3, both contributions are suppressed at the ~50 nm scale. These predictions fall within the reach of modern extreme ultraviolet thermal grating techniques. The authors also provide preliminary results on dynamical thermal conductivity (frequency-dependent response), showcasing the method’s potential for analyzing transient thermal grating experiments.

In summary, this work establishes a comprehensive and computationally tractable framework based on the WTE to model heat transport in the regime where phonon coherences are essential. It provides novel predictions of size effects and dynamical behavior in complex materials, offering a powerful new tool for interpreting experiments and designing materials for nanoscale thermal management.