There is great interest in finding materials possessing quasiparticles with topological properties. Such materials may have novel excitations that exist on their boundaries which are protected against disorder. We report experimental evidence that magnons in an insulating kagome ferromagnet can have a topological band structure. Our neutron scattering measurements further reveal that one of the bands is flat due to the unique geometry of the kagome lattice. Spin wave calculations show that the measured band structure follows from a simple Heisenberg Hamiltonian with a Dzyaloshinkii-Moriya interaction. This serves as the first realization of an effectively two-dimensional topological magnon insulator-a new class of magnetic material that should display both a magnon Hall effect and protected chiral edge modes. DOI: 10.1103/PhysRevLett.115.147201 PACS numbers: 75.30.Ds When quantum particles are confined to move in reduced dimensions, such as in planes, unexpectedly rich physics can emerge as a result of the geometry and interactions. The quantum Hall effect is a famous example, which results from placing a two-dimensional (2D) gas of electrons or quasiparticles in a large magnetic field [1]. Pioneering theoretical work by Haldane showed that some systems may inherently possess topological bands that allow them to exhibit quantum Hall physics without applied magnetic fields [2]. The discovery of materials in which strong spin-orbit coupling leads to topological bands, such as topological insulators, has led to a flurry of activity in condensed matter physics research [3,4]. Recently, theoretical studies have focused on 2D topological band structures that include flat bands due to the possibility of achieving fractional quantum hall physics in the absence of magnetic fields [5]. Flat bands (bands that are dispersionless in energy) hold unique interest because the interaction energy between particles may dominate the kinetic energy, leading to novel correlated electron states. A number of theoretical models for the fractional quantum Hall effect have been proposed based on flat topological bands [6][7][8]; however, these invariably require tuning of parameters, which is difficult to control in real materials.Topological band structures are not unique to systems with electronlike quasiparticles. It has been demonstrated that topological photon modes can be realized in experimental systems [9][10][11]. Possible realizations of topological bosonic systems that include flat bands have been proposed using dipolar molecules trapped in an optical lattice [12], and using photonic lattices [13] based on the interaction between photons and arrays of superconducting circuits [14], although experimental confirmation has yet to be demonstrated. In this Letter, we show that topological bands exist for another class of quasiparticles: magnons in an insulating ferromagnet. Our material serves as the first realization of an effectively 2D topological magnon insulator [15], an electrically insulating state in which the spin degre...

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