# Ballistic and hydrodynamic magnetotransport in narrow channels

## TL;DR

This paper theoretically explores how magnetic fields differentiate ballistic and hydrodynamic charge transport in narrow channels, revealing distinct signatures in the transverse electric field and non-local correlations.

## Contribution

It introduces a kinetic equation approach to identify magnetic field effects on ballistic and hydrodynamic transport, highlighting the limitations of hydrodynamic models with magnetic fields.

## Key findings

- Transverse electric field $E_y$ is locally enhanced with sharp directional anisotropy.
- Curvature of $E_y$ has opposite signs in ballistic and hydrodynamic regimes at weak magnetic fields.
- Distinct peaks in the transverse field indicate non-local correlations.

## Abstract

An increasing number of low carrier density materials exhibit a surprisingly large transport mean free path due to inefficient momentum relaxation. Consequently, charge transport in these systems is markedly non-ohmic but rather ballistic or hydrodynamic, features which can be explored by driving current through narrow channels. Using a kinetic equation approach we theoretically investigate how a non-quantizing magnetic field discerns ballistic and hydrodynamic transport, in particular in the spatial dependence of the transverse electric field, $E_y$: We find that $E_y$ is locally enhanced when the flow exhibits a sharp directional anisotropy in the non-equilibrium density. As a consequence, at weak magnetic fields, the curvature of $E_y$ has opposite signs in the ballistic and hydrodynamic regimes. Moreover, we find a robust signature of the onset of non-local correlations in the form of distinctive peaks of the transverse field, which are accessible by local measurements. Our results demonstrate that a purely hydrodynamic approach is insufficient in the Gurzhi regime once a magnetic field is introduced.