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This review formalizes the theoretical frameworks governing spatial and temporal thermal phonon coherence in materials engineered with artificial periodicity and structural disorder. By addressing the breakdown of conventional, particle-like Boltzmann transport in nanoscale lattices, the authors reconcile conflicting thermal conductivity phenomena reported across experimental literature. The result is a unified physical framework defining how phase correlations and wave-like interference govern heat dissipation in complex materials.
Standard particle-based heat transport breaks down inside engineered nanomaterials, and this framework finally unifies spatial and temporal phonon wave coherence to explain why.
As scientists seek to transcend traditional material property relationships, novel structures with artificial periodicity, configurational complexity, and disorder are increasingly being explored. For phonons, these architectures can induce significant phase correlations, which strongly shifts lattice heat conduction away from the conventional framework of particle-like scattering. This thermal phonon coherence can develop in space and time separately, resulting in distinct wave-like phenomena. Here we rigorously outline the theories of phonon spatial and temporal coherence. Crucially, this review focuses on demystifying and building conceptual understanding of the fundamental principles linking the various thermal conductivity and phonon property results reported in the literature. Furthermore, we use this understanding to establish a comprehensive physical picture of the wave nature of thermal phonons, unifying the spatial and temporal coherence theories. Altogether, the theoretical dissections in this review provide an extensive knowledge base for understanding and engineering thermal phonons in complex materials.