Abstract
We investigated the electronic structure of Na${}_{2}$IrO${}_{3}$ using optical spectroscopy, first-principles calculation, and x-ray absorption spectroscopy. We found that the electronic structure of Na${}_{2}$IrO${}_{3}$ is mainly determined by anisotropic hopping interactions and spin-orbit coupling. Due to the hopping interaction, the orbital character of the bands near the Fermi level deviates from the spin-orbit coupling-induced ${J}_{\mathrm{eff}}$ $=$ 1/2 states. Polarization-dependent O 1$s$ x-ray absorption spectroscopy showed that the ${J}_{\mathrm{eff}}$ $=$ 1/2 state of an Ir atom can be mixed with the ${J}_{\mathrm{eff}}$ $=$ 3/2 state of the neighboring Ir atom. This result implies that mixing between the ${J}_{\mathrm{eff}}$ $=$ 1/2 and 3/2 states in the valence state should be carefully considered in proposed exotic states of Na${}_{2}$IrO${}_{3}$, such as topological insulator and quantum spin liquid states.
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