Viscosity Bound Violation in Viscoelastic Fermi Liquids

Abstract

The anti-de Sitter/conformal field theory correspondence (AdS/CFT) has been used to determine a lower bound on the ratio of shear viscosity $\left(\eta\right)$ to entropy density $(s)$ for strongly-coupled field theories with a gravity dual. The conjectured universal lower bound, given as $\eta/s\geq\hbar/4\pi k_B$, is a measure of interaction strength in a quantum fluid where equality indicates a perfect quantum fluid. In this paper we study $\eta/s$ in a Fermi gas in the unitary limit. We show that in addition to a local minimum for $\eta/s$ at $T\approx 2T_c$ which obeys the lower bound, a more interesting result exists in the violation of the $\eta/s$ lower bound due to the superfluid fluctuations above $T_c$. To conclude, we examine the viscoelastic properties of the unitary Fermi gas. Previous work brought to light the connection between violation of the $\eta/s$ bound and a viscoelastic response in the context of holographic solids. We ultimately find that, in addition to holographic solids, all Fermi liquids with a viscoelastic response produced by superfluid fluctuations can violate the universal $\eta/s$ lower bound.