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