The interactions that lead to the emergence of superconductivity in iron-based materials remain a subject of debate. It has been suggested that electron-electron correlations enhance electron-phonon coupling in iron selenide (FeSe) and related pnictides, but direct experimental verification has been lacking. Here we show that the electron-phonon coupling strength in FeSe can be quantified by combining two time-domain experiments into a "coherent lock-in" measurement in the terahertz regime. X-ray diffraction tracks the light-induced femtosecond coherent lattice motion at a single phonon frequency, and photoemission monitors the subsequent coherent changes in the electronic band structure. Comparison with theory reveals a strong enhancement of the coupling strength in FeSe owing to correlation effects. Given that the electron-phonon coupling affects superconductivity exponentially, this enhancement highlights the importance of the cooperative interplay between electron-electron and electron-phonon interactions.

Experimental evidence on high-T c cuprates reveals ubiquitous charge density wave (CDW) modulations 1-10 , which coexist with superconductivity. Although the CDW had been predicted by theory 11-13 , important questions remain about the extent to which the CDW influences lattice and charge degrees of freedom and its characteristics as functions of doping and temperature. These questions are intimately connected to the origin of the CDW and its relation to the mysterious cuprate pseudogap 10,14 . Here, we use ultrahigh-resolution resonant inelastic X-ray scattering to reveal new CDW character in underdoped Bi 2.2 Sr 1.8 Ca 0.8 Dy 0.2 Cu 2 O 8+δ . At low temperature, we observe dispersive excitations from an incommensurate CDW that induces anomalously enhanced phonon intensity, unseen using other techniques. Near the pseudogap temperature T * , the CDW persists, but the associated excitations significantly weaken with an indication of CDW wavevector shift. The dispersive CDW excitations, phonon anomaly, and analysis of the CDW wavevector provide a comprehensive momentumspace picture of complex CDW behaviour and point to a closer relationship with the pseudogap state.With sufficient energy resolution, resonant inelastic X-ray scattering (RIXS) can be an ideal probe for revealing the CDW excitations in cuprates. By tuning the incident photon energy to the Cu L 3 -edge (Fig. 1a), the resonant absorption and emission processes can leave the system in excited final states, which couple to a variety of excitations arising from orbital, spin, charge, and lattice degrees of freedom 15 . Thus, information of these elementary excitations in energy and momentum space can be deduced from analysing the RIXS spectra as functions of the energy loss and the momentum transfer of the photons (Fig. 1a). This is highlighted by the pivotal role that RIXS has recently played in revealing orbital and magnetic excitations in cuprates [16][17][18][19][20] . In addition, RIXS provided the first X-ray scattering evidence for an incommensurate CDW in (Y,Nd)Ba 2 Cu 3 O 6+δ (ref. 4), owing to energy resolution that separated the quasi-elastic CDW signal (bright spot in Fig. 1b, limited by the instrumental resolution ∼130 meV) from other intense higher-energy excitations. Notably this quasi-elastic signal is asymmetric with respect to zero energy loss (Fig. 1c), which indicates the possible existence of additional low-energy excitations near the CDW wavevector (Q CDW ).In this work, we exploit the newly commissioned ultrahighresolution RIXS instrument at the European Synchrotron Radiation Facility to reveal these low-energy excitations near the CDW. We choose the double-layer cuprate Bi 2.2 Sr 1.8 Ca 0.8 Dy 0.2 Cu 2 O 8+δ (Bi2212), whose electronic structure has been extensively studied by surface-sensitive spectroscopy, such as scanning tunnelling microscopy 21 and angle-resolved photoemission 22 , and in which a short-range CDW order was recently reported 7,8 . With improved energy resolution up to 40 meV, we see additional features in the pre...

High temperature cuprate superconductors consist of stacked CuO2 planes, with primarily two dimensional electronic band structures and magnetic excitations [1,2], while superconducting coherence is three dimensional. This dichotomy highlights the importance of out-of-plane charge dynamics, believed to be incoherent in the normal state [3,4], yet lacking a comprehensive characterization in energy-momentum space. Here, we use resonant inelastic x-ray scattering (RIXS) with polarization analysis to uncover the pure charge character of a recently discovered collective mode in electron-doped cuprates [5-7]. This mode disperses along both the in-and, importantly, out-of-plane directions, revealing its three dimensional nature. The periodicity of the out-of-plane dispersion corresponds to the CuO2 plane distance rather than the crystallographic c-axis lattice constant, suggesting that the interplane Coulomb interaction drives the coherent out-of-plane charge dynamics. The observed properties are hallmarks of the long-sought acoustic plasmon, predicted for layered systems [8-13] and argued to play a substantial role in mediating high temperature superconductivity [13-15]. The charge dynamics of systems with periodically stacked quasi-two dimensional (2D) conducting planes are drastically affected in the presence of poorly screened interplane Coulomb interactions. In a simple layered electron gas model with conducting planes separated by dielectric spacers [8-10], the dispersion of plasmons, the collective electronic modes of the charge dynamics, evolves from optical-like to acoustic-like as a function of out-of-plane momentum qz [Fig. 1(a)], a behavior distinct from that in either pure 2D or isotropic 3D systems.For superconducting cuprates, similar charge dynamics have been postulated since they consist of conducting CuO2 planes stacked along the c-axis with poor out-of-plane screening [11][12][13]. While plasmons were observed in various spectroscopic studies at the Brillouin zone center [4,16,17] and by transmission electron energy loss spectroscopy (EELS) typically exploring in-plane