Shear Viscosity at the Ising-Nematic Quantum Critical Point in Two-Dimensional Metals

Abstract

In an isotropic strongly interacting quantum liquid without quasiparticles, general scaling arguments imply that the dimensionless ratio (kB/ℏ)η/s, where η 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: η scales in the same manner as a chiral conductivity, and the ratio η/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.