Hall effect in slip flow of two-dimensional electron fluid

Hall effect in high-mobility 2D mesoscopic samples with hydrodynamic electron transport is related to manifestation of non-dissipative Hall viscosity at classical magnetic fields. However, the latter can be obscured by the particular geometry of the electronic flow through constriction and boundary effects. In this work we consider the low-field Hall resistivity of the narrow channel with hydrodynamic electron transport. Using kinetic theory we show that the hydrodynamic Hall viscosity contribution is accompanied by the comparable ballistic contribution associated with the formation of Knudsen layers in the slip flow of 2D electron fluid. The studied ballistic correction is present at any specularity of the boundary reflection and lowers the magnitude of the total negative size-dependent correction to the bulk Hall resistivity. The obtained analytic expression for the total Hall resistivity can be used to estimate the boundary reflection coefficient in high-mobility structures.