High-temperature copper oxide superconductors consist of stacked CuO2 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 state3,4 within the limited range of momenta accessible by optics. Here 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 oxides5,6,7 reveals their charge origin, that is, without mixing with magnetic components5,6,7. 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 CuO2 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 systems8,9,10,11,12 and argued to play a substantial part in mediating high-temperature superconductivity10,11,12.
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This work is supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515. L.C. acknowledges support from the Department of Energy, SLAC Laboratory Directed Research and Development funder contract under DE-AC02-76SF00515. RIXS data were taken at beamline ID32 of the European Synchrotron Radiation Facility (ESRF, Grenoble, France) using the ERIXS spectrometer designed jointly by the ESRF and the Politecnico di Milano. G.G. and Y.Y.P. were supported by the by ERC-P-ReXS project (2016-0790) of the Fondazione CARIPLO and Regione Lombardia, in Italy. R.L.G. and T.S. acknowledge support from NSF award DMR-1708334. Computational work was performed on the Sherlock cluster at Stanford University and on resources of the National Energy Research Scientific Computing Center, supported by the US DOE under contract number DE-AC02-05CH11231.
Nature thanks D. M. Casa, D. van der Marel and the other anonymous reviewer(s) for their contribution to the peer review of this work.