Thermal Transport

Abstract

A common way to understand the heat transfer is by considering that energy is transferred by a quantum called phonon. A phonon is a pseudo-particle with energy $\hbar \omega$ and crystalline momentum $\hbar \mathbf q$ obtained from the solution of the equations of motion of the atoms in a periodic crystal lattice. With this building blocks the first picture of thermal transport is that of phonons moving randomly at their constant group velocity in a Brownian motion. The macroscopic consequence of this microscopic picture is a diffusive heat transport governed by the Fourier law. This law has been successfully used in the last two centuries, but in the last decades divergences from classical behavior at reduced time and length scales have been observed. The first approach to understand these deviations was using an effective thermal conductivity depending on the characteristic length of the samples, but still relying in the Fourier equation. This approach has also been overtaken in the last years using more advanced techniques. Some examples are ultra-fast laser techniques measuring the effective thermal conductivity using heaters with different sizes or working at different excitation frequency ranges [1,2,3,4,5,6,7]. In these new setups an explicit generalization of the Fourier law should be used because the effective thermal conductivity approach does not provide good results. In consequence, other transport phenomena such as ballistic transport, superdiffusive regime or collective flow have appeared [8,9,10,11,12].