Raman Scattering Signatures of Kitaev Spin Liquids in $A_2{\mathrm{IrO}}_3$ Iridates with $A=\mathrm{Na}$ or Li

We show how Raman spectroscopy can serve as a valuable tool for diagnosing quantum spin liquids (QSL). We find that the Raman response of the gapless QSL of the Kitaev-Heisenberg model exhibits signatures of spin fractionalization into Majorana fermions, which give rise to a broad signal reflecting their density of states, and $Z_2$ gauge fluxes, which also contribute a sharp feature. We discuss the current experimental situation and explore more generally the effect of breaking the integrability on response functions of Kitaev spin liquids.

Figure 1

A honeycomb lattice is shown in panel (a). Shaded yellow region indicates the unit cell with two sites $A$ and $B$. Three inequivalent nearest-neighbor bonds $x,y,z$, are shown in red, green, and blue. The problem of calculating the Raman response in the presence of Heisenberg terms can be mapped onto a local quantum quench, where four adjoining $Z_2$ fluxes, shown as gray hexagons, are inserted. The contribution from the nearest-neighbor ${\sigma }_{A\mathbf{r}}^y{\sigma }_{B\mathbf{r}}^y$ interactions along the $z$ bond, which flips the sign of the link variables is shown as green dashed bonds. Panel (b) displays the density of states $N(\omega )$ of Majorana fermions in the ground state flux sector.

Figure 2

The Raman response $I(\omega )$ (black curve) and its separate contributions (here $J_K=10J_H$). The Kitaev contribution $I_K(\omega )$, shown in green, is independent of the photon polarization and shows characteristic features of the matter fermion density of states, including the linear onset at low energies and the band edge at $12J_K$, note an additional factor of 2 in Eq. (6). The van Hove singularity at $2J_K$ is seen as a small dip at $4J_K$ (due to a discontinuity of the derivative). The zero and two-particle responses, $I_H^{[0]}(\omega )$ and $I_H^{[2]}(\omega )$, of the Heisenberg contribution are shown in blue and red (dashed line), respectively. A $\delta$-function peak occurs at the four flux gap ${\mathrm{\Delta }}_F=0.446J_K$, while the frequency dependence of the two-particle contribution reflects the local two-particle density of states in the presence of four fluxes. The overall polarization dependence of $I_H(\omega )$ on the relative angle $\theta$ between incoming and outgoing photons is shown in the inset. Accordingly, $I_K(\omega )$ only has contributions from the doublet $E_g$-symmetry component, while $I_H(\omega )$ has both $A_{1g}$ and $E_g$.