Topological phonons in two-dimensional materials

Phonons, the most fundamental emergent bosons in condensed matter systems, play an essential role in crystalline materials' thermal, mechanical, and electronic properties. Recently, the concept of topology has been introduced to phonon systems, and the nontrivial topological states also exist in phonons due to the constraint by the crystal symmetry of the space group. Although the classification of various topological phonons has been enriched theoretically, experimental studies were limited to several three-dimensional (3D) single crystals with inelastic X-ray or neutron scatterings. The experimental evidence of topological phonons in two-dimensional (2D) materials is absent. Using high-resolution electron energy loss spectroscopy following our theoretical predictions, we directly map out the phonon spectra of the atomically thin graphene in the entire 2D Brillouin zone and observe two nodal-ring phonons and four Dirac phonons. The closed loops of nodal-ring phonons and the conical structure of Dirac phonons in 2D momentum space are revealed by our measurements, in good agreement with our theoretical calculations.