Non-Fourier phonon heat conduction at the microscale and nanoscale

Phonon heat conduction at the microscale and the nanoscale exhibits rich phenomena beyond the predictions of Fourier's law, rivalling the phenomena of electrons. This Review discusses phonon heat conduction regimes, including the Casimir-Knudsen size effect, hydrodynamic transport, coherent transport (from quantization and localization) and divergence. The description of phonon heat conduction has typically been based on Fourier diffusion theory. However, over the past three decades, a host of interesting phonon transport phenomena beyond the Fourier diffusion picture have drawn much attention. Although most of the studies focused on classical size effects that lead to reduced thermal conductivity, other phenomena have been observed, often at the microscale and nanoscale, that are either completely novel or appear only at elevated temperatures. Examples are the prediction and observation of phonon second sound at high temperatures, quantized heat conduction and Anderson localization. These developments reveal rich phonon heat conduction phenomena analogous to those of electrical conduction. This Review discusses different non-Fourier heat conduction regimes (including the Casimir-Knudsen classical size effect regime), phonon hydrodynamics, the coherent phonon transport regimes (including localization and quantization of heat conduction) and the possibility of divergent heat conduction in low dimensions.

Automated summary

Phonon heat conduction at the microscale and nanoscale exhibits complex phenomena beyond the traditional predictions of Fourier's law, attracting wide attention. The development in studying phonon heat conduction phenomena reveals that besides classical size effects, other novel phenomena have emerged, often occurring at microscale and nanoscale, or only at elevated temperatures.