Photon-based spectroscopies have played a central role in exploring the electronic properties of crystalline solids and thin films. Though they remain a powerful tool for probing the electronic properties of nanostructures, they are limited by lack of spatial resolution. On the other hand, electron-based spectroscopies, e.g., electron-energy-loss spectroscopy (EELS) are now capable of sub-Angstrom spatial resolution. Core-loss EELS, a spatially-resolved analog of X-ray absorption, has been used extensively in the study of inhomogeneous complex systems. In this paper, we demonstrate that low-loss EELS in an aberration-corrected scanning transmission electron microscope, which probes low-energy excitations, combined with a theoretical framework for simulating and analyzing the spectra, is a powerful tool to probe low-energy electron excitations with atomic-scale resolution. The theoretical component of the method combines densityfunctional-theory (DFT) based calculations of the excitations with dynamical scattering theory for the electron beam. We apply the method to monolayer graphene in order to demonstrate that atomic-scale contrast is inherent in low-loss EELS even in a perfectly periodic structure. The method is a complement to optical spectroscopy as it probes transitions entailing momentum transfer. The theoretical analysis identifies the spatial and orbital origins of excitations, holding the promise of ultimately becoming a powerful probe of the structure and electronic properties of individual point and extended defects in both crystals and inhomogeneous complex nanostructures. The method can be extended to probe magnetic and vibrational properties with atomic resolution.
I. INTRODUCTIONOptical spectroscopies along with energy-band theory were the cornerstones upon which modern solid-state physics was founded. Ultraviolet and X-ray photoemission spectroscopies (UPS and XPS) were subsequently instrumental in the field of surface science. X-ray emission and absorption spectra (XAE and XAS) and their many variants, e.g., resonant x-ray scattering, have also played significant roles in probing the electronic properties of solids. Infrared absorption has been a powerful probe of phonons and lowenergy electronic excitations. The spatial resolution of these spectroscopies, however, is quite limited by the respective photon wavelengths and other factors.[1,2] Nevertheless, they continue to make major contributions in the study of nanostructures.Electron-based spectroscopies have the advantage of ultrasmall de Broglie wave lengths, which enable high spatial resolution. Scanning transmission electron microscopes (STEMs) employ a highly focused electron beam, which produces direct images of crystalline films with atomic resolution. The primary imaging mode of the STEM is Z-contrast imaging, which relies on high-angle Rutherford scattering by atomic nuclei [3]. The intensity of scattered electrons is proportional to approximately the square of the atomic number Z. In addition, inelastic scattering of the foc...