  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, based on
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 dramatic 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
novel materials, including a detailed mapping of isotope distributions.
