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