Non-local hydrodynamic transport and collective excitations in Dirac fluids

TL;DR

This paper investigates non-local hydrodynamic transport and collective excitations in Dirac fluids, revealing how angular harmonic scattering modes influence charge and thermal conductivities, and identifying novel damped collective modes.

Contribution

It provides exact expressions for non-local conductivities and uncovers new collective excitations arising from angular harmonic scattering in Dirac fluids.

Findings

Exact formulas for non-local charge and thermal conductivities.

Identification of non-degenerate damped collective modes.

Analysis of Dirac fluid transport in various geometries.

Abstract

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 non-local transport in the hydrodynamic regime is governed by infinite set of kinetic modes that describe non-collinear scattering events in different angular harmonic channels. The scattering rates of these modes $\tau_{m}^{-1}$ increase as $\|m\|$, where $m$ labels the angular harmonics. In an earlier publication, we pointed out that this dependence leads to anomalous, L\'evy-flight-like phase space diffusion (Phys. Rev. Lett. 123, 195302 (2019)). Here, we show how this surprisingly simple, non-analytic dependence allows us to obtain exact expressions for the non-local charge and electronic thermal conductivities. The peculiar dependence of the scattering rates on $m$ also leads to a non-trivial structure of collective excitations: Besides the well known plasmon, second sound and diffusive modes, we find non-degenerate 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.