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 numbersand frequencies in the hydrodynamic regime. We find that nonlocal transport in the hydrodynamic regime isgoverned by an infinite set of kinetic modes that describe noncollinear scattering events in different angularharmonic channels. The scattering rates of these modesτ−1mincrease as|m|,wheremlabels the angularharmonics. In an earlier publication, we pointed out that this dependence leads to anomalous, Lévy-flight-likephase space diffusion [Kiselev and Schmalian,Phys.Rev.Lett.123, 195302 (2019)]. Here, we show how thissurprisingly simple, nonanalytic dependence allows us to obtain exact expressions for the nonlocal charge andelectronic thermal conductivities. The peculiar dependence of the scattering rates onmalso leads to a nontrivialstructure of collective excitations: Besides the well-known plasmon, second-sound, and diffusive modes, we findnondegenerate damped modes corresponding to excitations of higher angular harmonics. We use these results toinvestigate the transport of a Dirac fluid through Poiseuille-type geometries of different widths and to study theresponse to surface acoustic waves in graphene-piezoelectric devices