Hall viscosity, anisotropy & internal angular momentum*

Inspired by recent hydrodynamic experiments on graphene and chiral active fluids, we examine the viscous response of systems in two spatial dimensions, allowing for anisotropy and internal spin degrees of freedom [1]. Though there are generally six non-dissipative (Hall) viscosities, we show there are only three independent Hall contributions to the viscous force density, meaning three components are redundant. We describe a similar redundancy for dissipative viscosities, and present hydrodynamic implications of this for pipe flows and free surface waves. Turning our attention to quantum systems on the lattice, we extend the Kubo formalism for viscosity to systems with internal degrees of freedom and discrete translational symmetry, and highlight the importance of properly considering internal angular momentum through some examples. Lastly, we mention an extension of our formalism to three dimensions and describe a novel viscosity coefficient that can emerge in magnetic crystals with cubic symmetry.

[1] Rao, P. & Bradlyn, B. Hall viscosity in quantum systems with discrete symmetry: point group and lattice anisotropy. Phys. Rev. X 10, 021005 (2020)