# The Hall effect in ballistic flow of two-dimensional interacting particles

## TL;DR

This paper investigates the Hall effect in ballistic, two-dimensional interacting particle systems, revealing unique behaviors of the Hall coefficient and electric field influenced by particle densities and interactions, with implications for high-mobility quantum systems.

## Contribution

It provides a theoretical analysis of the Hall effect in ballistic regimes of 2D charged particles, highlighting differences from disordered systems and exploring effects of inter-particle scattering.

## Key findings

- Hall coefficient is half of that in disordered samples for one-component systems.
- Hall electric field depends linearly on electron-hole concentration difference near neutrality.
- Corrections due to inter-particle scattering influence magnetoresistance and Hall field dependencies.

## Abstract

In high-quality solid-state systems at low temperatures, the hydrodynamic or the ballistic regimes of heat and charge transport are realized in the electron and the phonon systems. In these regimes, the thermal and the electric conductance of the sample can reach abnormally large magnitudes. In this paper, we study the Hall effect in a system of interacting two-dimensional charged particles in a ballistic regime. We demonstrated that the Hall electric field is caused by a change in the densities of particles due to the effect of external fields on their free motions between the sample edges. In one-component (electron or hole) systems the Hall coefficient turns out to one half compared with the one in conventional disordered Ohmic samples. This result is consistent with the recent experiment on measuring of the Hall resistance in ultra-high-mobility GaAs quantum wells. In two-component electron-hole systems the Hall electric field depends linearly on the difference between the concentrations of electrons and holes near the charge neutrality point (the equilibrium electron and hole densities coincide) and saturates to the Hall field of a one-component system far from the charge neutrality point. We also studied the corrections to magnetoresistance and the Hall electric field due to inter-particle scattering being a precursor of forming a viscous flow. For the samples shorter than the inter-particle scattering length, the obtained corrections govern the dependencies of magnetoresistance and the Hall field on temperature.