Electronic structure of Na$_{x}$CoO$_{2}$ investigated by X-ray absorption spectroscopy with Ab initio calculation*

The soft X-ray absorption spectra (XAS) of Na$_{x}$CoO$_{2}$ revealed marked and puzzling polarization dependence. It can not be explained by the degeneracy of e$_{g}$ states generally believed in Na$_{x}$CoO$_{2}$. We fabricated the thin films of x = 0.68 and x = 0.75 to investigate the polarization dependence of XAS. Within the first principles DFT calculations, we have explanations for this phenomenon. After the analysis of the DOS of Na$_{x}$CoO$_{2}$, we presume that the pre-edge peaks at 529 eV and 530 eV of Na$_{x}$CoO$_{2}$ O-$K$ edge may be not solely due to the unoccupied states of Co3+ and Co4+ eg states, but also due to the spacial asymmetry in the occupied Co 3d orbitals. Due to the hybridization between Co 3d {\&} O 2p orbitals, the p$_{x,y}$ and p$_{z}$ states will be non-degenerate.