Hall effect in a ballistic flow of two-dimensional interacting particles

In high-quality conductors, the hydrodynamic or the ballistic regimes of heat and charge transport can be realized at low temperatures. We study the Hall effect in a system of interacting two-dimensional charged particles in a narrow ballistic sample in a weak magnetic field. In such a system, the Hall electric field is mainly caused by redistribution of the particles moving between the longitudinal sample edges along the ballistic collisionless trajectories. Our consideration is based on solving the classical kinetic equation in the ballistic regime with taking into account the interparticle scattering and the magnetic force by the perturbation theory. In a one-component (electron or hole) system, the Hall coefficient turns out to be one-half of the Hall coefficient of conventional wide Ohmic samples. We argue that this result is apparently consistent with the recent measurements of the Hall resistance in ultra-high-mobility GaAs quantum wells. In a two-component electron-hole system, the Hall coefficient depends linearly on the difference n(0)(e) - n(0)(h) between the electron and the hole equilibrium densities n(0)(e) and n(0)(h) near the charge neutrality point (n(0)(e) = n(0)(h)) and saturates to the Hall coefficient of a one-component system far from the charge neutrality point (n(0)(e) >> n(0)(h) or n(0)(e) << n(0)(h)). We also studied the corrections from the interparticle scattering to magnetoresistance and the Hall effect, being the precursors of forming the viscous or the Ohmic flows.