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We performed a resonant inelastic X-ray scattering (RIXS) study ofLa$_{2-x}$Sr$_{x}$NiO$_{4+{\delta}}$ (LSNO) at the oxygen $K$ edge toinvestigate the nature of the doped holes with regard to charge excitations.Charge excitations of the hole-doped nickelates are found to be almostindependent of momentum transfer, indicating that the doped holes are stronglylocalized in character. Additionally, conspicuous changes in energy positionare in temperature dependence. These characters are observed in stark contrastto those of the high-$T_{c}$ cuprate La$_{2-x}$Sr$_{x}$CuO$_{4}$ (LSCO), wheredelocalized doped holes form charge excitations with sizable momentumdependence in the CuO$_2$ plane. This distinct nature of charge excitations ofdoped holes is consistent with the metallicity of the materials and could becaused by strong electron-phonon coupling and weak quantum spin fluctuation inthe nickelates.

Localized character of charge excitations for La$_{2-x}$Sr$_{x}$NiO$_{4+{\delta}}$ revealed by oxygen $K$-edge resonant inelastic X-ray scattering