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We have investigated the excitation spectra of $j_{eff}$=$\frac{1}{2}$ Mottinsulator Na$_2$IrO$_3$. Taking into account a relativistic multiplet structureof Ir ions, we have calculated the optical conductivity $\sigma(\omega)$ andresonant inelastic x-ray scattering (RIXS) spectra, which manifest differentfeatures from those of a canonical $j_{eff}$=$\frac{1}{2}$ systemSr$_2$IrO$_4$.Distinctly from the two-peak structure in Sr$_2$IrO$_4$,$\sigma(\omega)$ in Na$_2$IrO$_3$ has a broad single peak dominated byinterband transitions from $j_{eff}$=$\frac{3}{2}$ to $\frac{1}{2}$. RIXSspectra exhibit the spin-orbit (SO) exciton that has a two-peak structurearising from the crystal-field effect, and the magnon peak at energies muchlower than in Sr$_2$IrO$_4$. In addition, a small peak near the opticalabsorption edge is found in RIXS spectra, originating from the coupling betweenthe electron-hole ($e$-$h$) excitation and the SO exciton. Our findingscorroborate the validity of the relativistic electronic structure andimportance of both itinerant and local features in Na$_2$IrO$_3$.

Electronic excitations in the edge-shared relativistic Mott insulator: Na$_2$IrO$_3$