Electron energy-loss spectroscopy of quasi-two-dimensional crystals: Beyond the energy-loss functions formalism

TL;DR

This paper develops a unified theoretical framework for electron energy-loss spectroscopy (EELS) of quasi-2D materials, accounting for both electronic response and probe kinematics, revealing complex interactions like plasmon coupling.

Contribution

It introduces a comprehensive theory beyond the traditional energy-loss functions formalism, specifically tailored for quasi-2D crystals, incorporating both scattering types and experimental configurations.

Findings

Strong coupling between plasmon excitation and elastic resonances in graphene.

The new theory accurately describes EELS spectra of quasi-2D materials.

Traditional formalism is insufficient for interpreting EELS in these systems.

Abstract

A consistent theory of electron energy-loss spectroscopy (EELS) includes two indispensable elements: (i) electronic response of the target system and (ii) quantum kinematics of probing electrons. While for the bulk materials and their surfaces separating these two aspects and focusing on the former is the usual satisfactory practice (the energy-loss functions formalism), we show that, for quasi-2D crystals, the interplay of the system's electronic response and the details of the probe's motion affects EEL spectra dramatically, and it must be taken into account for the reliable interpretation of the experiment. To this end, we come up with a unified theory which, on the same footing, treats both the long- and short-range scattering, within both the transmission and reflection experimental setups. Our calculations performed for graphene reveal a phenomenon of a strong coupling between the $\pi+\sigma$ plasmon excitation and elastic {\it scattering resonances}. Freed from the conventions of the energy-loss functions formalism, our theory serves as a consistent and systematic means of the understanding of the EELS of quasi-2D materials.