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Thermal transport at the nanoscale level is attracting attention not only because of its physically interesting features such as the peculiar behavior of phonons due to their pronounced ballistic and wave-like properties but also because of its potential applications in alleviating heat dissipation problems in electronic and optical devices and thermoelectric energy harvesting. In the last quarter-century, researchers have elucidated the thermal transport properties of various nanostructured materials, including phononic crystals (PnCs): artificial periodic structures for phonons. PnCs are excellent platforms for investigating thermal transport owing to their well-defined structural parameters. In addition, it is interesting to control thermal transport by interference, as demonstrated in the low-frequency regime with elastic waves and sounds. In this article, we focus on high-frequency phonons and review the thermal transport in semiconductor PnCs. This comprehensive review provides an understanding of recent studies and trends, organized as theoretical and experimental, in terms of the quasiparticle and wave aspects.
Nomura et al. (Sat,) studied this question.