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

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.

minor typos fixed

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• Anatomy of plasmons in generic Luttinger semimetals
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