Hydrodynamic model for electron-hole plasma in graphene

We propose a hydrodynamic model describing steady-state and dynamic electron and hole transport properties of graphene structures which accounts for the features of the electron and hole spectra. It is intended for electron-hole plasma in graphene characterized by high rate of inter-carrier scattering compared to external scattering (on phonons and impurities), i.e., for intrinsic or optically pumped (bipolar plasma), and gated graphene (virtually monopolar plasma). We demonstrate that the effect of strong interaction of electrons and holes on their transport can be treated as a viscous friction between the electron and hole components. We apply the developed model for the calculations of the graphene dc conductivity; in particular, the effect of mutual drag of electrons and holes is described. The spectra and damping of collective excitations in graphene in the bipolar and monopolar limits are found. It is shown that at high gate voltages and, hence, at high electron and low hole densities (or vice-versa), the excitations are associated with the self-consistent electric field and the hydrodynamic pressure (plasma waves). In intrinsic and optically pumped graphene, the waves constitute quasineutral perturbations of the electron and hole densities (electron-hole sound waves) with the velocity being dependent only on the fundamental graphene constants.