Analytical model for non-linear magnetotransport in viscous electron fluid

Abstract

We develop an analytical theoretical model for non-linear hydrodynamic magnetotransport of two-dimensional (2D) electron fluid with strong pair correlations in the electron dynamics. Within 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 Non-Newtonian behavior of the fluid. We analytically calculate flow profiles in long samples in a stationary highly non-linear regime and the corresponding magnetoresistance. Pair correlations lead to a characteristic non-monotonic dependence of the differential resistance on magnetic field. We compare our results with experimental data on non-linear magnetotransport of high-purity GaAs quantum wells; we conclude that our model can be responsible for a part of the observed features of the differential magnetoresistance.