Viscosity Bound Violation in Viscoelastic Fermi Liquids

TL;DR

This paper investigates the shear viscosity to entropy density ratio in a unitary Fermi gas, revealing violations of the universal lower bound due to superfluid fluctuations and connecting viscoelastic properties to bound violations.

Contribution

It demonstrates that Fermi liquids with viscoelastic responses from superfluid fluctuations can violate the universal ta/s lower bound, extending previous holographic insights.

Findings

ta/s ratio can violate the lower bound above T_c due to superfluid fluctuations.

A local minimum of ta/s at T ew T_c obeys the bound.

Viscoelastic response is linked to bound violation in 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.