Third-order optical conductivity of an electron fluid

TL;DR

This paper derives the universal third-order optical conductivity of an isotropic electron fluid in the hydrodynamic regime, providing explicit formulas for Dirac materials and predicting observable nonlinear optical effects.

Contribution

It introduces a universal form of third-order nonlinear optical conductivity in the hydrodynamic regime for electron fluids, with explicit formulas for Dirac materials.

Findings

Universal third-order conductivity formula derived

Explicit expressions for graphene and Weyl semimetals

Predictions for third-harmonic generation and birefringence

Abstract

We derive the nonlinear optical conductivity of an isotropic electron fluid at frequencies below the interparticle collision rate. In this regime, governed by hydrodynamics, the conductivity acquires a universal form at any temperature, chemical potential, and spatial dimension. We show that the nonlinear response of the fluid to a uniform field is dominated by the third-order conductivity tensor $\sigma^{(3)}$ whose magnitude and temperature dependence differ qualitatively from those in the conventional kinetic regime of higher frequencies. We obtain explicit formulas for $\sigma^{(3)}$ for Dirac materials such as graphene and Weyl semimetals. We make predictions for the third-harmonic generation, renormalization of the collective-mode spectrum, and the third-order circular magnetic birefringence experiments.