Abstract
By incorporating a long-range Coulomb interaction into the framework of the one-band Hubbard model, we delineate how the low-energy plasmon around $1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, which is a universal feature of the charge dynamics of the cuprates, manifests itself in the resonant inelastic x-ray scattering (RIXS) spectra. The long-range Coulomb interaction in the doped system controls the form of the intraband RIXS dispersion near the Brillouin zone center around the $\ensuremath{\Gamma}$ point. The out-of-plane momentum transfer component ${q}_{z}$ is found to play a key role in determining whether or not the RIXS spectrum shows a plasmon-related gap at $\ensuremath{\Gamma}$.
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