Hydrodynamic model for electron-hole plasma in graphene

Abstract

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 intercarrier 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.

Hydrodynamics in graphene: Linear-response transport

“…Leading corrections to the Fermi-liquid results can be described in terms of small deviations of the energy and imbalance currents from their limiting values (10). It is intuitively clear that the imbalance current approaches the limiting value exponentially.…”

“…At the same time, due to the classical nature of the Coulomb interaction between charge carriers in graphene, the system is also non-Lorentz-invariant [6][7][8]12,13]. As a result, the standard derivation [1,10,12,13] of the hydrodynamic equations has to be revisited [5][6][7].…”

“…[4,6,8,11]), or j and P (see Refs. [9,10]). Our three-mode hydrodynamics is applicable for any value of doping providing us with a unified approach to electronic transport in graphene.…”

“…Recently, the kinetic equation approach was applied to electronic excitations in graphene [4][5][6][7][8][9][10][11]. In contrast to conventional metals and semiconductors, graphene is characterized by a linear excitation spectrum, which makes the system explicitly non-Galilean-invariant [6][7][8]12,13].…”

“…[9,10] and then extended to double-layer graphene-based structures in Ref. [11], which allowed for a description of the Coulomb drag effect [16][17][18][19] in graphene.…”