Phonon-Mediated Hydrodynamic Transport in Weyl Semimetals

In light of recent experimental and numerical analyses, we study through a simple microscopic model the role that electron-electron interactions mediated by virtual phonons can play in inducing a hydrodynamic regime in Weyl semimetals. The electric and thermal conductivities are obtained and, similarly to interactions with real phonons, they display a different scaling with temperature (T) depending on whether T lies above of below the Bloch-Grünesen temperature (T_BG). For T > T_BG the virtual phonons act on-shell, and a modified temperature-independent Lorenz ratio is obtained. At low temperatures T < T_BG, the system manifests a T² behavior for the electric and thermal scattering times. In addition, it is seen that chirality-violating interactions play a crucial role in inducing electric current relaxation through Baber scattering. We put our theory in context of experimental results.