Phonon heat transport in low-dimensional materials departs from the classical Boltzmann picture when structural length scales approach phonon wavelengths, coherence lengths, or mean free paths. In this regime, enhanced phase correlation enables wave-based phenomena, notably coherent transport in periodic architectures and Anderson localization in disordered media. This review summarizes recent progress in understanding these effects and their impact on thermal conductivity.
We first discuss coherent phonon transport in artificial periodic systems, including superlattices and phononic crystals. Experiments and simulations commonly report non-monotonic thermal conductivity versus period length, reflecting the interplay between coherent interference and incoherent scattering. Spectral analyses further indicate that coherent transport is dominated by low-frequency phonons, while higher frequency modes are strongly suppressed by anharmonicity.
We then examine phonon Anderson localization in low-dimensional disordered materials. Localization emerges when the localization length becomes shorter than relevant transport lengths. Its impact to thermal conductivity depends critically on spectral overlap with heat-carrying phonons, making localization a selective rather than universal mechanism for thermal suppression.
Finally, we outline open challenges, including quantifying the competition between interference and inelastic scattering, and realizing experimentally observable localization effects at room temperature. Overall, this review provides a wave-based framework for phonon transport in low-dimensional materials and offers guidance for phonon engineering via coherence and disorder.