Odd viscosity in the quantum critical region of a holographic Weyl semimetal

TL;DR

This paper investigates odd viscosity in a holographic Weyl semimetal model, revealing that the mixed axial gravitational anomaly induces non-zero odd viscosities at the quantum critical point, with some viscosities violating the KSS bound.

Contribution

It demonstrates that the mixed axial gravitational anomaly leads to non-zero odd viscosities in a holographic Weyl semimetal at the quantum critical point, a novel transport phenomenon.

Findings

Both odd viscosities are non-vanishing in the quantum critical region.

One anisotropic shear viscosity violates the KSS bound.

Viscosity and conductivity physics are governed by the quantum critical point.

Abstract

We study odd viscosity in a holographic model of a Weyl semimetal. The model is characterised by a quantum phase transition from a topological semimetal to a trivial semimetal state. Since the model is axisymmetric in three spatial dimensions there are two independent odd viscosities. Both odd viscosity coefficients are non-vanishing in the quantum critical region and non-zero only due to the mixed axial gravitational anomaly. It is therefore a novel example in which the mixed axial gravitational anomaly gives rise to a transport coefficient at first order in derivatives at finite temperature. We also compute anisotropic shear viscosities and show that one of them violates the KSS bound. In the quantum critical region, the physics of viscosities as well as conductivities is governed by the quantum critical point.