Three-dimensional collective charge excitations in electron-doped copper oxide superconductors
High-temperature copper oxide superconductors consist of stacked CuO 2 planes, with electronic band structures and magnetic excitations that are primarily two-dimensional1,2, but with superconducting coherence that is three-dimensional. This dichotomy highlights the importance of out-of-plane charge dynamics, which has been found to be incoherent in the normal state within the limited range of momenta accessible by optics. Here in this study, we use resonant inelastic X-ray scattering to explore the charge dynamics across all three dimensions of the Brillouin zone. Polarization analysis of recently discovered collective excitations (modes) in electron-doped copper oxides reveals their charge origin, that is, without mixing with magnetic components. The excitations disperse along both the in-plane and out-of-plane directions, revealing its three-dimensional nature. The periodicity of the out-of-plane dispersion corresponds to the distance between neighbouring CuO 2 planes rather than to the crystallographic c-axis lattice constant, suggesting that the interplane Coulomb interaction is responsible for the coherent out-of-plane charge dynamics. The observed properties are hallmarks of the long-sought ‘acoustic plasmon’, which is a branch of distinct charge collective modes predicted for layered systems and argued to play a substantial part in mediating high-temperature superconductivity.