Topological phonons in graphene

By means of first-principles calculations and a modeling analysis, we have predicted that traditional two-dimensional graphene hosts four types of topological phononic Dirac points (DPs) and a phononic nodal ring (PNR) in its phonon spectrum. In the phonon spectrum of graphene, there exist four types of DPs, DP1, DP2, DP3, and DP4, with both DP1 and DP2 located at the Brillouin zone (BZ) corners K and K', DP3 located along the Gamma-K line, and DP4 located along the Gamma-M line, as well as the PNR surrounding the centered Gamma point in the q(x,y) plane. The calculations further reveal that Berry curvatures are vanishingly zero throughout the whole BZ, except for the positions of these four Dirac phonons, at which the nonzero singular Berry curvatures appear with a Berry phase of pi or -pi, confirming its topological nontrivial nature. The topologically protected nontrivial phononic edge states have been also evidenced along both the zigzag-edged and armchair-edged boundaries. These results may pave the way for further studies of the topological phononic properties of graphene, such as phononic destructive interference with a suppression of backscattering and intrinsic phononic quantum Hall-like effects.