Direct measurement of topologically protected nontrivial phononic edge states

Topological phonons associated with nontrivial edge states open a new avenue to explore interesting quasi-particles excitations and manipulate phonon transportations. Although kinds of topological phonons associated with their promising device applications have been theoretically predicted, experimentally observing nontrivial edge states is still absent owing mainly to the challenges in simultaneously achieving sufficient sensitivity and space, momentum, and energy resolutions for detecting the highly localized edge phonon mode. Here, with delicately balanced space and momentum resolutions of electron energy loss spectroscopy in a scanning transmission electron microscope, we realize the direct observation of topologically nontrivial phononic edge states of graphene in momentum and real space. Two types of two-fold degenerate edge states, induced respectively by Dirac point and nodal ring, are explicitly observed at the Brillouin zone boundary M point, and highly localized at the edge in real space, which are in excellent agreement with the theoretical predictions. The verification of topological phononic edge states and the demonstrated detection method are crucial to the field of topological phonons, promoting quasiparticles-phonon coupling explorations, thermal transportation studies, and novel phonon device developments.