Probing mesoscopic crystals with electrons: One-step simultaneous inelastic and elastic scattering theory

Vladimir U. Nazarov, Vyacheslav M. Silkin, Eugene E. Krasovskii

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9 Scopus citations

Abstract

Inelastic scattering of the medium-energy (∼10-100 eV) electrons underlies the method of the high-resolution electron energy-loss spectroscopy (HREELS), which has been successfully used for decades to characterize pure and adsorbate-covered surfaces of solids. With the emergence of graphene and other quasi-two-dimensional (Q2D) crystals, HREELS could be expected to become the major experimental tool to study this class of materials. We, however, identify a critical flaw in the theoretical picture of the HREELS of Q2D crystals in the context of the inelastic scattering only ("energy-loss functions" formalism), in contrast to its justifiable use for bulk solids and surfaces. The shortcoming is the neglect of the elastic scattering, which we show is inseparable from the inelastic one, and which, affecting the spectra dramatically, must be taken into account for the meaningful interpretation of the experiment. With this motivation, using the time-dependent density functional theory for excitations, we build a theory of the simultaneous inelastic and elastic electron scattering at Q2D crystals. We apply this theory to HREELS of graphene, revealing an effect of the strongly coupled excitation of the π+σ plasmon and elastic diffraction resonances. Our results open a path to the theoretically interpretable study of the excitation processes in crystalline mesoscopic materials by means of HREELS, with its supreme resolution on the meV energy scale, which is far beyond the capacity of the now overwhelmingly used EELS in transmission electron microscopy.

Original languageAmerican English
Article number235414
JournalPhysical Review B
Volume96
Issue number23
DOIs
StatePublished - 11 Dec 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 American Physical Society.

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