Out-of-bounds hydrodynamics in anisotropic Dirac fluids

We study the hydrodynamic behavior in two-dimensional, interacting electronic systems with merging Dirac points at charge neutrality. The dispersion along one crystallographic direction is Dirac-like, while it is Newtonian-like in the orthogonal direction. As a result, two diverging length scales emerge giving rise to highly anisotropic hydrodynamic transport coefficients. The electrical conductivity exhibits the metallic temperature dependence if the external electric field is applied in the direction of the Dirac-like linear dispersion and the insulating one in the orthogonal direction. The shear viscosity is a fourth-rank tensor with distinct elements exhibiting fundamentally different scaling with temperature, depending on the direction of the momentum flow. Most dramatically, we find a violation of the famous lower bound for the shear viscosity to entropy density ratio. Our results are of importance for oxide heterostructures and organic charge transfer salts.

Arxiv: 1708.02759