Origin of the high-energy charge excitations observed by resonant inelastic x-ray scattering in cuprate superconductors

The recent development of x-ray scattering techniques revealed the charge-excitation spectrum in high-$T_c$ cuprate superconductors. While the presence of a dispersive signal in the high-energy charge-excitation spectrum is well accepted in the electron-doped cuprates, its interpretation and universality are controversial. Since charge fluctuations are observed ubiquitously in cuprate superconductors, the understanding of its origin is a pivotal issue. Here, we employ the layered $t$-$J$ model with the long-range Coulomb interaction and show that an acoustic-like plasmon mode with a gap at in-plane momentum (0,0) captures the major features of the high-energy charge excitations. The high-energy charge excitations, therefore, should be a universal feature in cuprate superconductors and are expected also in the hole-doped cuprates. Acoustic-like plasmons in cuprates have not been recognized yet in experiments. We propose several experimental tests to distinguish different interpretations of the high-energy charge excitations.