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The topological physics has been extensively studied in different kinds ofbosonic and fermionic systems, ranging from artificial structures to naturalmaterials. However, the coexistence of topological phonon and electron in onesingle material is seldom reported. Recently, graphdiyne is proposed to be atwo-dimensional (2D) electronic second-order topological insulator (SOTI). Inthis work, based on density-functional tight-binding calculations, we foundthat graphdiyne is equivalent to the Kekule lattice, also realizing a 2Dphononic SOTI in both out-of-plane and in-plane modes. Depending on edgeterminations, the characterized topological corner states can be either insideor outside the bulk gap, which are tunable by local corner potential. Mostremarkably, a unique selectivity of space and symmetry is revealed inelectron-phonon coupling between the localized phononic and electronictopological corner states. Our results not only demonstrate the phononichigher-order band topology in a real carbon material, but also provide anopportunity to investigate the interplay between phononic and electronichigher-order topological states.

Kekule Lattice in Graphdiyne: Coexistence of Phononic and Electronic Higher-Order Band Topology