Analytical model for nonlinear magnetotransport in a viscous electron fluid

We develop an analytical theoretical model for nonlinear hydrodynamic magnetotransport of two-dimensional (2D) electron fluids with strong pair correlations in electron dynamics. Within the classical kinetics of 2D electrons, such correlations are described as subsequent ``extended'' collisions of the same electrons, temporarily joined in pairs. Corresponding correlation-induced retarded terms in the fluid dynamic equations can be described for slow flows as the dependence of the electron fluid viscosity on the flow velocity gradient, that is, a non-Newtonian behavior of the fluid. We analytically calculate flow profiles in long samples in a stationary highly nonlinear regime and the corresponding magnetoresistance. Pair correlations lead to a characteristic nonmonotonic dependence of the differential resistance on the magnetic field. We compare our results with experimental data on nonlinear magnetotransport of high-purity GaAs quantum wells; we conclude that our model can be responsible for some of the observed features of the differential magnetoresistance.