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We calculate the Raman response for the Kitaev spin model on the$\mathcal{H}$-$0$, $\mathcal{H}$-$1$, and $\mathcal{H}$-$\infty$ harmonichoneycomb lattices. We identify several quantitative features in the Ramanspectrum that are characteristic of the spin liquid phase. Unlike the dynamicalstructure factor, which probes both the Majorana spinons and flux excitationsthat emerge from spin fractionalization, the Raman spectrum in the Kitaevmodels directly probes a density of states of pairs of fractional, dispersingMajorana spinons. As a consequence, the Raman spectrum in all these models isgapless for sufficiently isotropic couplings, with a low-energy power law thatresults from the Fermi lines (or points) of the dispersing Majorana spinons. Weshow that the polarization dependence of the Raman spectrum contains crucialinformation about the symmetry of the ground state. We also discuss to whatextent the features of the Raman response that we find reflect genericproperties of the spin liquid phase, and comment on their possible relevance to$\alpha-$, $\beta-$ and $\gamma-$Li$_2$IrO$_3$ compounds.

Theory of Raman response in three-dimensional Kitaev spin liquids: application to $\beta-$ and $\gamma-$Li$_2$IrO$_3$ compounds