Hydrodynamic electron transport near charge neutrality

We develop theory of hydrodynamic electron transport in a long-range disorder potential for conductors in which the underlying electron liquid lacks Galilean invariance. For weak disorder we express the transport coefficients in terms of the intrinsic kinetic coefficients of the electron liquid and the correlation function of the disorder potential. We apply these results to analyze the doping- and temperature-dependence of transport coefficients of graphene devices. We show that at charge neutrality long range disorder increases the conductivity of the system above the intrinsic value, due to the predominantly vortical flow caused by local deviations from charge neutrality. Its magnitude is inversely proportional to the shear viscosity of the electron liquid and scales as the square of the disorder correlation radius. This is qualitatively different from the situation away from charge neutrality. In that case the flow is predominantly potential, and produces negative viscous contributions to the conductivity.