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

Hugo Lourenço-Martins,Mathieu Kociak

doi:10.1103/physrevx.7.041059

Abstract

Recently, two reports have demonstrated the amazing possibility to probe vibrational excitations from nanoparticles with a spatial resolution much smaller than the corresponding free-space phonon wavelength using electron energy loss spectroscopy (EELS). While Lagos et al. evidenced a strong spatial and spectral modulation of the EELS signal over a nanoparticle, Krivanek et al. did not. Here, we show that discrepancies among different EELS experiments as well as their relation to optical near- and far-field optical experiments can be understood by introducing the concept of confined bright and dark Fuchs-Kliewer modes, whose density of states is probed by EELS. Such a concise formalism is the vibrational counterpart of the broadly used formalism for localized surface plasmons; it makes it straightforward to predict or interpret phenomena already known for localized surface plasmons such as environment-related energy shifts or the possibility of 3D mapping of the related surface charge densities.

Highlights

Two reports [Krivanek et al Nature (London) 514, 209 (2014), Lagos et al Nature (London) 543, 529 (2017)] have demonstrated the amazing possibility to probe vibrational excitations from nanoparticles with a spatial resolution much smaller than the corresponding free-space phonon wavelength using electron-energy-loss spectroscopy (EELS)
Electron-energy-loss spectroscopy experiments consist of sending a free-electron beam onto a sample of interest and retrieving information on its excitations through the analysis of the energy lost by the electron beam
It can essentially be performed without spatial resolution at low electron energy (HREELS) or with a sub-angstrom resolution in a scanning transmission electron microscope (STEM)

Summary

Published by the American Physical Society

Method (BEM) [7,8,9] and discrete dipole approximation [10]] have been extensively used to simulate optical and EELS spectra dominated by localized SPs confined on nanoparticles. This makes extinction and absorption cross sections almost identical at the low energy of the phonon regime, making EELS very close to the absorption cross section for dipolar cSPh modes (see the analytical proof in the Appendix) We note that this contrasts with the case of a silver plasmonic nanorod of the same size (see Fig. 3). Due to the large free-space wavelength of the cSPh compared to typical dimensions of nano-objects, the QS approximation holds essentially true for submicron nanoparticles, and any nanoparticle can be described by a series of eigencharges and related λi that depends only on the shape of the nanoparticle This theory works well for understanding cSPhs, but will obviously fail to describe long-wavelength, propagating surface phonons that may arise in the particular case of very large particle or slabs. Mode λi ω [from Eq (1)] ω (simulations, this paper) ω (simulations, Ref. [11]) ω (experiments, Ref. [11])

Not applicable Not applicable

Given the similarities pointed out in the paper between