Nonlocal hydrodynamic transport and collective excitations in Dirac fluids

We study the response of a Dirac fluid to electric fields and thermal gradients at finite wave numbers and frequencies in the hydrodynamic regime. We find that nonlocal transport in the hydrodynamic regime is governed by an infinite set of kinetic modes that describe noncollinear scattering events in different angular harmonic channels. The scattering rates of these modes τ−1m increase as | m | , where m labels the angular harmonics. In an earlier publication, we pointed out that this dependence leads to anomalous, Lévy-flight-like phase space diffusion [Kiselev and Schmalian, Phys. Rev. Lett. 123, 195302 (2019)]. Here, we show how this surprisingly simple, nonanalytic dependence allows us to obtain exact expressions for the nonlocal charge and electronic thermal conductivities. The peculiar dependence of the scattering rates on m also leads to a nontrivial structure of collective excitations: Besides the well-known plasmon, second-sound, and diffusive modes, we find nondegenerate damped modes corresponding to excitations of higher angular harmonics. We use these results to investigate the transport of a Dirac fluid through Poiseuille-type geometries of different widths and to study the response to surface acoustic waves in graphene-piezoelectric devices.