Gapped collective charge excitations and interlayer hopping in cuprate superconductors

We use resonant inelastic x-ray scattering (RIXS) to probe the propagation of plasmons in the electron-doped cuprate superconductor Sr${}_{0.9}$La${}_{0.1}$CuO${}_2$ (SLCO). We detect a plasmon gap of $\sim$~120 meV at the two-dimensional Brillouin zone center, indicating that low-energy plasmons in SLCO are not strictly acoustic. The plasmon dispersion, including the gap, is accurately captured by layered $t$-$J$-$V$ model calculations. A similar analysis performed on recent RIXS data from other cuprates suggests that the plasmon gap is generic and its size is related to the magnitude of the interlayer hopping $t_z$. Our work signifies the three-dimensionality of the charge dynamics in layered cuprates and provides a new method to determine $t_z$.