Shear Viscosity in a Non-Fermi Liquid Phase of a Quadratic Semimetal

TL;DR

This paper investigates the shear viscosity in a scale-invariant, non-Fermi liquid phase of quadratic semimetals, revealing a universal ratio of shear viscosity to entropy density consistent with quantum bounds.

Contribution

The authors develop a kinetic equation approach to compute shear viscosity in a non-Fermi liquid phase, highlighting its universal behavior at quantum criticality.

Findings

Shear viscosity to entropy density ratio is universal.

The ratio is consistent with gauge-gravity duality bounds.

Transport dominated by collision processes in the non-Fermi liquid phase.

Abstract

We study finite temperature transport in the Luttinger-Abrikosov-Beneslavskii phase -- an interacting, scale invariant, non-Fermi liquid phase found in quadratic semimetals. We develop a kinetic equation formalism to describe the d.c. transport properties, which are dominated by collisions, and compute the shear viscosity $\eta$. The ratio of shear viscosity to entropy density $\eta/s$ is a measure of the strength of interaction between the excitations of a quantum fluid. As a consequence of the quantum critical nature of the system, $\eta / s$ is a universal number and we find it to be consistent with a bound proposed from gauge-gravity duality.