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Vibrational Surface Electron-Energy-Loss Spectroscopy Probes Confined Surface-Phonon Modes

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Phonons are vibration waves that propagate in solids. Their study and quantification is fundamental for understanding many material properties, from superconductivity to thermoelectricity. Numerous techniques have been developed for studying phonons, such as high-resolution electron-energy-loss spectroscopy (HREELS), in which electrons are sent toward an object of interest, and the energy of the phonons is deduced from that lost by the electrons. Recently, HREELS has been pushed to the nanometer scale. With the success of these experiments, researchers now want to determine what types of phonons are being measured and how to rationalize some of the observations. A similar problem once arose in HREELS experiments on electronic waves known as plasmons, experiments that were interpreted at the time using analogies with phonons. In a recent paper published in PRX, we show that, in a reversal of traditional analogies, current phonon experiments can now be interpreted using modern concepts for plasmons. Most of the properties of surface plasmons in nano-objects can be understood by introducing a rigorous quasiclassic eigenmode decomposition, which we have adapted to the case of surface phonons. From this decomposition, all classical and linear optical properties of phonons can be deduced, such as optical cross sections, EELS probabilities, and the electromagnetic local density of states. Such a theory describes most of the recent observations, such as the energy of phonons in slabs of silica or the spatial modulation of surface phonons in cubes of magnesium oxide. It also permits researchers to bridge optical and EELS observations. With the rise of new HREELS instrumentation able to probe phonons at the nanometer scale, this theory will help us to grasp the physics of forthcoming experiments, as well as predict new effects such as 3D mapping of surface phonons.