Electron Hydrodynamics of Graphene from a First-Principles GW Approach: Electronic Compressibility, Backflows and Transport Coefficients*

Doped graphene at low temperatures has experimental signatures of hydrodynamic behavior originating from the electron-electron interaction. Here, we use the GW approximation to study the electronic and thermal properties of graphene from first-principles within a Fermi liquid framework. We show how the electronic compressibility is modified by many-body contributions at finite temperature. Next, we solve the kinetic equation using an exact expression of the scattering matrix. We show how the commonly-used relaxation time approximation causes a severe underestimation of transport coefficients, and how a correct treatment of momentum dissipation is critical to the description of transport properties. We will present results for transport coefficients, including electrical conductivity, the electronic contribution to thermal conductivity and the viscosity coefficients, discussing corrections due to the interaction of carriers with the environment and the behavior of the electron liquid as a non-Newtonian fluid.