Hydrodynamic-to-ballistic crossover in Dirac fluid

TL;DR

This paper presents an exactly solvable kinetic model for Dirac materials like graphene, revealing how electron-electron and electron-hole collisions influence the transition from hydrodynamic to ballistic transport regimes and affect collective excitations.

Contribution

It introduces a universal measure of non-Galilean invariance and characterizes the behavior of plasmons and electron-hole sound across the crossover.

Findings

Relaxation rate of electric current due to e-e collisions is identified.

Electron-hole sound has low damping at neutrality but high damping with doping.

Plasmons become well-defined in doped samples due to damping behavior.

Abstract

We develop an exactly solvable classical kinetic model of transport in Dirac materials accounting for strong electron-electron (e-e) and electron-hole (e-h) collisions. We use this model to track the evolution of graphene conductivity and properties of its collective excitations across the hydrodynamic-to-ballistic crossover. We find the relaxation rate of electric current by e-e collisions that is possible due to the lack of Galilean invariance, and introduce a universal numerical measure of this non-invariance in arbitrary dimension. We find the two branches of collective excitations in the Dirac fluid: plasmons and electron-hole sound. The sound waves have small viscous damping at the neutrality point both in the hydrodynamic and ballistic regimes, but acquire large damping due to e-h friction even at slight doping. On the contrary, plasmons acquire strong frictional damping at the neutrality point and become well-defined in doped samples.