Nicholas Metropolis Award Talk: Hydrodynamics of Heat Transport in Crystals

Heat flux in nonmagnetic dielectric crystals is determined by the propagation of lattice vibrations and is often modeled with the kinetic gas theory, where phonons are the gas constituents. However, recent advancements have shown the limitations of this approximation, especially when dealing with crystals at cryogenic temperatures or 2D materials. In these cases, the behavior of the interacting phonon gas departs from conventional expectations and causes high thermal conductivity and hydrodynamic phenomena such as second sound, where heat propagates as a wave, rather than diffusively.
To explain these properties, we introduce a gas of collective phonon excitations called relaxons [1], defined as the eigenvectors of the scattering operator. The exact thermal conductivity from the linearized Boltzmann transport equation is still described by the kinetic gas theory, with the relevant gas consisting not of phonons, but of relaxons. Surface scattering is reinterpreted as a hydrodynamic effect [2] with friction at the materials borders slowing the heat flux, in analogy with the Poiseuille flow of water through a pipe. The dispersion relation of relaxons [3], obtained from the Fourier transform of the linearized Boltzmann equation, describes heat oscillations and provide a new interpretation of second sound. These considerations are applied to a first-principles study of graphene, MoS₂ and silicon, revising the relevant time, velocity and length scales of thermal transport and providing a new viewpoint on semiclassical transport theories.
[1] A. Cepellotti and N. Marzari, Phys. Rev. X 6, 041013 (2016)
[2] A. Cepellotti and N. Marzari, Nano Lett. 17, 4675 (2017)
[3] A. Cepellotti and N. Marzari, Phys. Rev. Mater. 1, 045406 (2017)