Non-Fourier phonon heat conduction at the microscale and nanoscale

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.