Unified Description of the Classical Hall Viscosity

In the absence of time-reversal symmetry, viscous electron flow hosts a number of interesting phenomena, of which we focus here on the Hall viscosity. Taking a step beyond the hydrodynamic definition of the Hall viscosity, we derive a generalized relation between the Hall viscosity and the transverse electric field using a kinetic equation approach. We explore two different geometries where the Hall viscosity is accessible to measurement. For hydrodynamic flow of electrons in a narrow channel, we find that the viscosity may be measured by a local probe of the transverse electric field near the center of the channel. Ballistic flow, on the other hand, is dominated by boundary effects. In a Corbino geometry, viscous effects arise not from boundary friction but from the circular flow pattern of the Hall current. In this geometry, we introduce a viscous Hall angle that remains well defined throughout the crossover from ballistic to hydrodynamic flow and captures the bulk viscous response of the fluid.