  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.
