Acoustic graphyne: A second-order real Chern topological insulator

Graphyne has recently attracted much attention since it is an important derivative of graphene with unique topological properties. Although graphyne is not a conventional topological insulator because of its weak spin–orbit coupling, it is a real Chern topological insulator with the higher-order topology. However, it lacks a realistic model. Here, we propose a schedule to realize acoustic graphyne. By introducing negative coupling to simulate the carbon–carbon triple bond, we realize the transition from trivial to higher-order topological phases, characterized by real Chern numbers. These topologically protected corner states are achieved in a finite-size sample, and the condition for their existence is discussed. Our research extends the concept of real Chern insulators and provides a platform for studying the topological properties of graphene-like structural compounds.