Unbounded Hydrodynamics in Nodal-Line Semimetals

The ratio between the shear viscosity and the entropy η/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 (hbar/(4π 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 η/s ∝T is unbounded, scaling towards zero with decreasing temperature T in the perturbative limit. We find that the hydrodynamic scattering time between collisions τ ~ hbar/(α² ν k_F), with (ν k_F) the energy scale set by the radius of the ring and α the fine structure constant. We suggest that the lower bound criteria should be modified to account for unscreened relativistic systems with a Fermi surface.