Counterflows in viscous electron-hole fluid

In ultra-pure conductors, collective motion of charge carriers at relatively high temperatures may become hydrodynamic such that electronic transport may be described similarly to a viscous flow. In confined geometries (e.g., in ultra-high quality nanostructures), the resulting flow is Poiseuille-like. When subjected to a strong external magnetic field, the electric current in semimetals is pushed out of the bulk of the sample towards the edges. Moreover, we show that the interplay between viscosity and fast recombination leads to the appearance of counterflows. The edge currents possess a non-trivial spatial profile and consist of two stripe-like regions: the outer stripe carrying most of the current in the direction of the external electric field and the inner stripe with the counterflow.