Transport in the non-Fermi liquid phase of isotropic Luttinger semimetals

TL;DR

This paper investigates the transport properties of the non-Fermi liquid phase in Luttinger semimetals, revealing unique optical conductivity behavior and the impact of disorder, with results aligning with experimental observations.

Contribution

It provides a detailed calculation of optical and dc conductivities in the non-Fermi liquid phase of Luttinger semimetals, highlighting hyperscaling violation and disorder effects.

Findings

Optical conductivity shows small hyperscaling violation in clean systems.

Weak disorder causes a strong power-law suppression of dc conductivity at low temperatures.

Disordered systems behave as power-law insulators, consistent with experiments.

Abstract

Luttinger semimetals have quadratic band crossings at the Brillouin zone-center in three spatial dimensions. Coulomb interactions in a model that describes these systems stabilize a non-trivial fixed point associated with a non-Fermi liquid state, also known as the Luttinger-Abrikosov-Beneslavskii phase. We calculate the optical conductivity $\sigma (\omega) $ and the dc conductivity $\sigma_{dc} (T) $ of this phase, by means of the Kubo formula and the Mori-Zwanzig memory matrix method, respectively. Interestingly, we find that $\sigma (\omega) $, as a function of the frequency $\omega$ of an applied ac electric field, is characterized by a small violation of the hyperscaling property in the clean limit, which is in marked contrast to the low-energy effective theories that possess Dirac quasiparticles in the excitation spectrum and obey hyperscaling. Furthermore, the effects of weak short-ranged disorder on the temperature-dependence of $\sigma_{dc} (T)$ give rise to a much stronger power-law suppression at low temperatures compared to the clean limit. Our findings demonstrate that these disordered systems are actually power-law insulators. Our theoretical results agree qualitatively with the data from recent experiments performed on Luttinger semimetal compounds like the pyrochlore iridates [ (Y$_{1-x}$Pr$_x$)$_2$Ir$_2$O$_7$ ].