Intrinsic charge and spin conductivities of doped graphene in the Fermi-liquid regime

The experimental availability of ultra-high-mobility samples of graphene opens the possibility to realize and study experimentally the hydrodynamic regime of the electron liquid. In this regime, the rate of electron-electron collisions is extremely high and dominates over the electron-impurity and electron-phonon scattering rates, which are therefore neglected. The system is brought to a local quasiequilibrium described by a set of smoothly varying (in space and time) functions, i.e., the density, the velocity field, and the local temperature. In this paper, we calculate the charge and spin conductivities of doped graphene due solely to electron-electron interactions. We show that, in spite of the linear low-energy band dispersion, graphene behaves in a wide range of temperatures as an effectively Galilean-invariant system: the charge conductivity diverges in the limit T -> 0, while the spin conductivity remains finite. These results pave the way to the description of charge transport in graphene in terms of Navier-Stokes equations.