Polarization dependent X-ray absorption and resonant inelastic X-ray scattering studies at Cu K-edge in quasi-one-dimensional cuprate LiCu$_{2}$O$_{2}$ single crystals

We have carried out a polarization dependent X-ray absorption (XAS) and the resonant inelastic X-ray scattering (RIXS) experiments on LiCu2O2 single crystals near the Cu K-edge. The XAS measurement reveals absorption peaks associated with Cu+ and Cu2+ 4$p$ unoccupied states respectively. A pre-edge peak can be assigned to quadrupole transition at the Cu2+ site. In the RXIS measurement, the incident energy dependent spectra disclose three energy loss peaks at 3.6 eV, 6.1 eV and 4.9 eV. The energy loss of 3.6 eV and 6.1 eV are the charge transfer states from O 2$p $nonbonding and bonding states to the Cu2+ 3$d $states and resonate at two incident energies. The third peak at 4.9 eV can be associated with Cu+ 4\textit{px,y}; we argue that this feature is generated by the Cu+ 3$d $state coupled with Cu2+ 3$d $state through the shared O 2$p $bonding. In addition, the 3.6 eV and 6.1 eV energy loss peaks are nearly dispersionless in momentum dependent spectra.