chapter  11

Thermal Transport and Phonon Coherence in Phononic Nanostructures

WithJuan Sebastian Reparaz, Markus R. Wagner

In the last century, a large diversity of research fields emerged targeting the fundamental and applied properties of the collective vibrations of lattice atoms of materials (phonons). Many works were driven by the discovery of inelastic light scattering as theoretically predicted by Brillouin 1 and experimentally shown by Raman 2 in the 1920s. After these discoveries, many works focused on unraveling the detailed structure of the vibrational spectrum of materials. As phonons are the main heat carriers in most nonmetallic materials, the study of the phononic properties of materials is closely linked to the study of the thermal properties and the propagation of heat. Although heat transport has been investigated for centuries, it is only with the advent of nanotechnology that advanced techniques have been developed to study its properties at the nanoscale. On macroscopic length scales and at temperatures over the Debye temperature (i.e., large phonon occupation), heat transport is usually explained using Fourier’s law, Q = −k∇T, where Q is the heat flux, κ is the thermal conductivity, and T is the temperature. However, at the nanoscale or at low temperatures (low-phonon occupation), deviations from this classic behavior occur due to the ballistic component of heat propagation, i.e., when the typical dimensions of the ρ material are comparable to the thermal phonon mean free path ∧th, which defines the average distance that thermal phonons can travel without being scattered.