Terahertz magneto-optical properties of graphene hydrodynamic electron liquid

The discovery of the hydrodynamic electron liquid (HEL) in graphene [D. Bandurin \emph{et al.}, Science {\bf 351}, 1055 (2016) and J. Crossno \emph{et al.}, Science {\bf 351}, 1058 (2016)] has marked the birth of the solid-state HEL which can be probed near room temperature in a table-top setup. Here we examine the terahertz (THz) magneto-optical (MO) properties of a graphene HEL. Considering the case where the magnetic length $l_B=\sqrt{\hbar/eB}$ is comparable to the mean-free path $l_{ee}$ for electron-electron interaction in graphene, the MO conductivities are obtained by taking a momentum balance equation approach on the basis of the Boltzmann equation. We find that when $l_B\sim l_{ee}$, the viscous effect in a HEL can weaken significantly the THz MO effects such as cyclotron resonance and Faraday rotation. The upper hybrid and cyclotron resonance magnetoplasmon modes $\omega_\pm$ are also obtained through the RPA dielectric function. The magnetoplasmons of graphene HEL at large wave-vector regime are affected by the viscous effect, and results in red-shifts of the magnetoplasmon frequencies. We predict that the viscosity in graphene HEL can affect strongly the magneto-optical and magnetoplasmonic properties, which can be verified experimentally.