Third-order optical conductivity of an electron fluid

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.

10 pages, 5 figures

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• Terahertz tuning of Dirac plasmons in Bi${}_2$Se${}_3$ Topological Insulator
• Nonlinear spectroscopy of collective modes in excitonic insulator
• The saddle-point exciton signature on high harmonic generation in 2D hexagonal nanostructures
• Acoustomagnetoelectric effect in two-dimensional materials: Geometric resonances and Weiss oscillations
• Revealing the frequency-dependent oscillations in the nonlinear terahertz response induced by the Josephson current
• Graphene as a source of entangled plasmons
• Dominant Role of Two-Photon Vertex in Nonlinear Response of Dirac Materials
• Four-wave mixing in Weyl semimetals
• Plasmonic quantum nonlinear Hall effect in noncentrosymmetric 2D materials
• Floquet engineering of many-body states by the ponderomotive potential
• Dipole excitation of collective modes in viscous two-dimensional electron systems
• Microscopic quantum description of second-order nonlinearities in 2D hexagonal nanostructures beyond the Dirac cone approximation