Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals

TL;DR

This paper calculates the shear viscosity at the Ising-nematic quantum critical point in 2D metals, revealing a divergence of the viscosity-to-entropy ratio at low temperatures due to anisotropic scaling effects.

Contribution

It provides the first computation of shear viscosity at this critical point using an expansion below dimension 2.5, highlighting anisotropic scaling violations.

Findings

The shear viscosity scales similarly to chiral conductivity.

The ratio η/s diverges as T^{-2/z} at low temperatures.

Anisotropy causes deviation from universal scaling expectations.

Abstract

In an isotropic strongly interacting quantum liquid without quasiparticles, general scaling arguments imply that the dimensionless ratio $(k_B /\hbar)\, \eta/s$, where $\eta$ is the shear viscosity and $s$ is the entropy density, is a universal number. We compute the shear viscosity of the Ising-nematic critical point of metals in spatial dimension $d=2$ by an expansion below $d=5/2$. The anisotropy associated with directions parallel and normal to the Fermi surface leads to a violation of the scaling expectations: $\eta$ scales in the same manner as a chiral conductivity, and the ratio $\eta/s$ diverges at low temperature ($T$) as $T^{-2/z}$, where $z$ is the dynamic critical exponent for fermionic excitations dispersing normal to the Fermi surface.