Theory of Atomic-Scale Vibrational Mapping and Isotope Identification with Electron Beams

Transmission electron microscopy and spectroscopy currently enable the acquisition of spatially resolved spectral information from a specimen by focusing beams down to sub-Angstrom spot then analyzing energy inelastically scattered electrons with few-meV resolution. This technique has recently been used experimentally resolve vibrational modes in 2D materials emerging at mid-infrared frequencies. Here, based on first-principles theory, we demonstrate possibility identifying single isotope atom impurities nanostructure through trace that they leave spatial characteristics modes. Specifically, examine hexagonal boron nitride molecule as an example application, which presence impurity is revealed dramatic changes spectra, well space-, energy-, momentum-resolved inelastic signal. We compare these results conventional far-field spectroscopy, showing offer superior resolution combined ability probe complete set modes, including those are optically dark. Our study relevant for atomic-scale characterization novel materials, detailed mapping distributions.