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 nonquantizing 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 nonequilibrium 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 nonlocal 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.

• Received 31 January 2019
• Revised 13 November 2019

DOI:https://doi.org/10.1103/PhysRevB.100.245305