Nonlocal transport in Weyl semimetals in the hydrodynamic regime

The nonlocal response of chiral electron fluid in a semi-infinite Weyl semimetal slab with the electric current source and drain attached to its surface is studied by using the consistent hydrodynamic framework. It is found that the Chern-Simons terms lead to a spatial asymmetry of the electron flow and the electric field. Most remarkably, the corresponding topological terms could result in a negative nonlocal resistance. In addition, they give rise to the anomalous Hall current, which is sensitive to the spatial distribution of the electric field in the plane of the contacts and depends on the orientation of the chiral shift.