Raman response and shear viscosity in the non-Fermi liquid phase of Luttinger semimetals

TL;DR

This paper investigates the Raman response and shear viscosity in the non-Fermi liquid LAB phase of Luttinger semimetals, proposing experimental signatures and analyzing emergent hyperscaling violations.

Contribution

It introduces the Raman response as a novel experimental probe and analyzes shear viscosity to understand the LAB phase's properties in Luttinger semimetals.

Findings

Raman response shows power-law behavior at high frequencies.

A quasi-elastic peak appears at low frequencies.

Shear viscosity to entropy density ratio indicates hyperscaling violation.

Abstract

Luttinger semimetals represent materials with strong spin-orbit coupling, harbouring doubly-degenerate quadratic band touchings at the Brillouin zone center. In the presence of Coulomb interactions, such a system exhibits a non-Fermi liquid phase [dubbed as the Luttinger-Abrikosov-Beneslavskii (LAB) phase], at low temperatures and zero doping. However, a clear experimental evidence of this emergent state remains elusive to this date. Hence, we focus on extracting the Raman response as a complementary experimental signature. At frequencies much larger than the temperature, the Raman response exhibits a power-law behavior, which can be verified experimentally. On the other hand, at lower frequencies, the Raman response displays a quasi-elastic peak. We also compute the ratio of the shear viscosity and the entropy density, and the value obtained is a consequence of the hyperscaling violation that emerges in the LAB phase.