Hydrodynamic transport in the Luttinger-Abrikosov-Beneslavskii non-Fermi liquid

TL;DR

This paper calculates the shear viscosity and electrical conductivity of the non-Fermi-liquid LAB phase in three-dimensional Luttinger semimetals, revealing universal ratios and the significance of Coulomb interactions and Auger processes.

Contribution

It provides the first determination of transport properties in the LAB phase using RG and Boltzmann methods, highlighting the role of Coulomb projection and Auger processes.

Findings

Universal viscosity over entropy ratio near the lower bound.

Electrical conductivity at the LAB fixed point.

Coulomb interaction projection and Auger processes significantly affect scattering.

Abstract

We determine the shear viscosity and the dc electrical conductivity of interacting three-dimensional Luttinger semimetals, which have a quadratic band touching point in the energy spectrum, in the hydrodynamic regime. It is well-known that when the chemical potential is right at the band touching point the long-range Coulomb interaction induces the Luttinger-Abrikosov-Beneslavskii (LAB) phase at T = 0, which is an interacting, scale-invariant, non-Fermi-liquid state of electrons. Upon combining the renormalization-group (RG) analysis near the upper critical spatial dimension of four with the Boltzmann kinetic equation, we determine the universal ratio of viscosity over entropy, and the electrical dc conductivity of the system at the interacting LAB fixed point of the RG flow. The projection of the Coulomb interaction on the eigenstates of the system is found to play an important quantitative role for the scattering amplitude in the collision integral, and the so-called Auger-processes make a large numerical contribution to the inverse scattering time in the transport quantities. The obtained leading order result suggests that the universal ratio of the viscosity over entropy, when extrapolated to the physical three spatial dimensions, is above, but could be rather close to, the Kovtun-Son-Starinets lower bound.