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

TL;DR

This paper calculates the Raman response in three-dimensional Kitaev spin liquids, revealing characteristic gapless features and polarization dependencies that can help identify spin liquid phases in iridate compounds.

Contribution

It provides a detailed theoretical analysis of the Raman spectrum in 3D Kitaev models, connecting spectral features to Majorana spinons and symmetry properties, with implications for real materials.

Findings

Raman spectrum is gapless with a low-energy power law due to Majorana spinons.

Polarization dependence reveals information about ground state symmetry.

Features may be relevant for identifying spin liquids in iridate compounds.

Abstract

We calculate the Raman response for the Kitaev spin model on the $\mathcal{H}$-$0$, $\mathcal{H}$-$1$, and $\mathcal{H}$-$\infty$ harmonic honeycomb lattices. We identify several quantitative features in the Raman spectrum that are characteristic of the spin liquid phase. Unlike the dynamical structure factor, which probes both the Majorana spinons and flux excitations that emerge from spin fractionalization, the Raman spectrum in the Kitaev models directly probes a density of states of pairs of fractional, dispersing Majorana spinons. As a consequence, the Raman spectrum in all these models is gapless for sufficiently isotropic couplings, with a low-energy power law that results from the Fermi lines (or points) of the dispersing Majorana spinons. We show that the polarization dependence of the Raman spectrum contains crucial information about the symmetry of the ground state. We also discuss to what extent the features of the Raman response that we find reflect generic properties of the spin liquid phase, and comment on their possible relevance to $\alpha-$, $\beta-$ and $\gamma-$Li$_2$IrO$_3$ compounds.