Position and momentum mapping of vibrations in graphene nanostructures in the electron microscope

Abstract: Propagating atomic vibrational waves, phonons, rule important thermal, mechanical, optoelectronic and transport characteristics of materials. Thus the knowledge of phonon dispersion, namely the dependence of vibrational energy on momentum is a key ingredient to understand and optimize the material's behavior. However, despite its scientific importance in the last decade, the phonon dispersion of a freestanding monolayer of two dimensional (2D) materials such as graphene and its local variations has still remained elusive because of experimental limitations of vibrational spectroscopy. Even though electron energy loss spectroscopy (EELS) in transmission has recently been shown to probe the local vibrational charge responses, these studies are yet limited to polar materials like boron nitride or oxides, in which huge signals induced by strong dipole moments are present. On the other hand, measurements on graphene performed by inelastic x-ray (neutron) scattering spectroscopy or EELS in reflection do not have any spatial resolution and require large microcrystals. Here we provide a new pathway to determine the phonon dispersions down to the scale of an individual freestanding graphene monolayer by mapping the distinct vibration modes for a large momentum transfer. The measured scattering intensities are accurately reproduced and interpreted with density functional perturbation theory (DFPT). Additionally, a nanometre-scale mapping of selected momentum (q) resolved vibration modes using graphene nanoribbon structures has enabled us to spatially disentangle bulk, edge and surface vibrations.