Unified Theory of Heat Flow in Semiconductors Beyond Textbook Fourier's Law

Classically, heat conduction in solids is described as a diffusion process, following Fourier's law of heat conduction, where thermal conductivity is considered a purely material property, independent of the sample geometry. Recent experiments have demonstrated a deviation from the Fourier's law at nano- to micro-scales, where heat conduction transitions from diffusion to quasiballistic or ballistic regimes. Furthermore, in ultrahigh thermal conductivity materials, heat flow transitions into a hydrodynamic second sound, where heat flows in a wave-like manner at cryogenic temperatures. However, due to the lack of an effective predictive tool, the observations of these exotic, unconventional non-Fourier regimes have been limited to only a handful of materials. Here, I will discuss our recently developed theoretical framework, which can accurately predict the material and geometric conditions required to observe these non-Fourier heat flow regimes in crystalline semiconductors (where heat is predominantly carried by phonons), using the spectral information of the phonon collision matrix. This framework will simplify the identification of thermal transport regimes, thus enabling rapid experimental exploration of unconventional heat transport regimes.