# Universal linear and nonlinear electrodynamics of the Dirac fluid

## TL;DR

This paper derives a universal relation between linear and nonlinear ac conductivities in Dirac fluids within the hydrodynamic regime, applicable across various systems and conditions, with specific predictions for graphene.

## Contribution

It introduces a universal theoretical framework linking linear and second-order nonlinear conductivities in Dirac systems, valid for diverse dispersions and conditions.

## Key findings

- Derived a universal relation for ac conductivities in Dirac fluids.
- Showed differences between hydrodynamic and kinetic regimes.
- Predicted photon drag and second-harmonic generation in graphene.

## Abstract

A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of the hydrodynamic nonlinear conductivity are shown to differ from their counterparts in the more familiar kinetic regime of higher frequencies. Due to universality of the hydrodynamic equations, the obtained formulas are valid for systems with an arbitrary Dirac-like dispersion, ranging from solid-state electron gases to free-space plasmas, either massive or massless, at any temperature, chemical potential or space dimension. Predictions for photon drag and second-harmonic generation in graphene are presented as one application of this theory.