Hall effect in Poiseuille flow of two-dimensional electron fluid

Abstract

The hydrodynamic regime of charge transport has been recently realized in high-quality conductors. In the hydrodynamic as well as in the Ohmic regimes the main part of the Hall resistance of a long sample is determined by the balance between the Lorentz force and the electric force, acting on conduction electrons. Experimentally observed deviations of the Hall resistance in hydrodynamic samples from such ``standard'' value are usually associated with the Hall viscosity term in the Navier-Stokes equation. In this work we theoretically study the Hall effect in a Poiseuille flow of a two-dimensional electron fluid. We show that the near-edge semiballistic layers with the width of the order of the interparticle mean-free path, which inevitably appear near sample edges, give the contribution to the Hall resistance which is comparable with the bulk contribution from the Hall viscosity. In this way, the measured deviations of the Hall resistance from the ``standard'' one in hydrodynamic samples by the usual contact techniques should be associated with both the Hall viscosity in the bulk and the semiballistic effects in the near-edge layers.