Observation of momentum-dependent charge excitations in hole-doped cuprates using resonant inelastic x-ray scattering at the oxygen <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math> edge

We investigate electronic excitations in ${\mathrm{La}}_{2\ensuremath{-}x}{(\mathrm{Br},\mathrm{Sr})}_{x}{\mathrm{CuO}}_{4}$ using resonant inelastic x-ray scattering (RIXS) at the oxygen $K$ edge. RIXS spectra of the hole-doped cuprates show clear momentum dependence below 1 eV. The broad spectral weight exhibits positive dispersion and shifts to higher energy with increasing hole concentration. Theoretical calculation of the dynamical charge structure factor on oxygen orbitals in a three-band Hubbard model is consistent with the experimental observation of the momentum and doping dependence, and therefore the momentum-dependent spectral weight is ascribed to intraband charge excitations which have been observed in electron-doped cuprates. Our results confirm that the momentum-dependent charge excitations exist on the order of the transfer energy ($t$), and the broad spectral line shape indicates damped and incoherent character of the charge excitations at the energy range in the doped Mott insulators.