Unbounded Hydrodynamics in Nodal-Line Semimetals

The ratio between the shear viscosity and the entropy $\eta/s$ is considered a universal measure of the strength of interactions in quantum systems. In relativistic systems, this quantity was conjectured to have a universal lower bound $(1/4\pi)\hbar/k_{B}$, which indicates a very strongly correlated quantum fluid. By solving the quantum kinetic theory for a nodal-line semimetal in the hydrodynamic regime, we show that $\eta/s\propto T$ is \emph{unbounded}, scaling towards zero with decreasing temperature $T$ in the perturbative limit. We find that the hydrodynamic scattering time between collisions $\tau\sim\hbar/\alpha^{2}vk_{F}$, with $vk_{F}$ the energy scale set by the radius of the ring and $\alpha$ the fine structure constant. We suggest that the lower bound criteria should be modified to account for unscreened relativistic systems with a Fermi surface.