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

TL;DR

This paper introduces a novel method to map phonon dispersion in individual graphene monolayers using electron microscopy, combining experimental measurements with density functional theory to resolve local vibrational modes.

Contribution

It presents a new approach for determining phonon dispersions at nanoscale resolution in 2D materials, overcoming previous experimental limitations.

Findings

Successful mapping of vibrational modes in graphene monolayers

Agreement between experimental data and density functional perturbation theory

Spatially resolved vibration modes in graphene nanoribbons

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.