Viscous electron magnetotransport properties near charge neutrality*

We focus on a magneto-hydrodynamic electron transport theory in conductors lacking Galilean invariance in the presence of long range disorder. We obtain perturbative results of transport coefficients for weak disorder and show their dependences on the intrinsic transport coefficients of the electron liquid and the correlation function of the disorder potential. At charge neutrality, the electron transport is strongly affected by the vortical hydrodynamic flow caused by the local charge densities, as opposed to the potential flow away from charge neutrality. We then apply our results to graphene near charge neutrality. In particular, we show that the magnetoresistance is positive and quadratic in weak magnetic field. The Hall resistivity is given by the classical Hall resistivity with a renormalization factor depending on the doping density, correlation function of the disorder potential and the shear viscosity. We also study magneto-thermal transport coefficients. We show that the magnetothermal conductivity is negative and quadratic in field. We also show the viscous and disorder effects for the Nernst coefficient and magneto-thermal power.