Phononic real Chern insulator with protected corner modes in graphynes

Higher-order topological insulators have attracted great research interest recently. Different from conventional insulators, higher-order do not necessarily require spin-orbit coupling, which makes it possible to realize them in spinless systems. Here, we study phonons 2D graphyne family materials. By using first-principle calculations and topology/symmetry analysis, find that both graphdiyne $\ensuremath{\gamma}$-graphyne exhibit a second-order topology, belongs the specific case known as real Chern insulator. We identify nontrivial phononic band gaps, are characterized by numbers enabled spacetime inversion symmetry. The protected phonon corner modes verified calculation on finite-size nanodisk. In addition, show 3D insulator state can be realized for graphdiyne. Our extends scope of topology spatially localized could useful novel applications.