  A comparative resonant inelastic x-ray scattering (RIXS) study of three
well-known Kitaev materials is presented: $\alpha$-Li$_2$IrO$_3$,
Na$_2$IrO$_3$, and $\alpha$-RuCl$_3$. Despite similar low-energy physics, these
materials show distinct electronic properties, such as the large difference in
the size of the charge gap. The RIXS spectra of the spin-orbit exciton for
these materials show remarkably similar three-peak features, including sharp
low energy peak (peak A) as well as transitions between $j_{\text{eff}}=1/2$
and $j_{\text{eff}}=3/2$ states. Comparison of experimental spectra with
cluster calculations reveals that the observed three-peak structure reflects
the significant role that non-local physics plays in the electronic structure
of these materials. In particular, the low-energy peak A arises from a
holon-doublon pair rather than a conventional particle-hole exciton as proposed
earlier. Our study suggests that while spin-orbit assisted Mott insulator is
still the best description for these materials, electron itinerancy cannot be
ignored when formulating low-energy Hamiltonian of these materials.
