Sound waves and resonances in electron-hole plasma

Abstract: Inspired by the recent experimental signatures of relativistic hydrodynamics in graphene, we investigate theoretically the behavior of hydrodynamic sound modes in such quasi-relativistic fluids near charge neutrality, within linear response. Locally driving an electron fluid at a resonant frequency to such a sound mode can lead to large increases in the electrical response at the edges of the sample, a signature which cannot be explained using diffusive models of transport. We discuss the robustness of this signal to various effects, including electron-acoustic phonon coupling, disorder, and long-range Coulomb interactions. These long range interactions convert the sound mode into a collective plasmonic mode at low frequencies unless the fluid is charge neutral. At the smallest frequencies, the response in a disordered fluid is quantitatively what is predicted by a "momentum relaxation time" approximation. However, this approximation fails at higher frequencies (which can be parametrically small), where the classical localization of sound waves cannot be neglected. Experimental observation of such resonances is a clear signature of relativistic hydrodynamics, and provides an upper bound on the viscosity of the electron-hole plasma.