Topological Dirac and chiral phonons in isotope-substituted single-layer and bilayer graphene

Topological phonons have attracted widespread attention for low-dissipation thermal transport. Most studies have obtained the topological phonon dispersion and edge states in two-dimensional (2D) materials, with limited exploration of the physical mechanisms of interlayer interaction and isotope substitution. Symmetry constrained Dirac phonons (DP) and chiral phonons (CP), capable of inducing intriguing edge states, offer an excellent platform for exploring these issues. We investigate the topological DP and CP of single-layer and bilayer graphene with an analytical tight-binding model supplemented by first-principles calculations. CP dispersion strongly depends on isotope substitution in contrast to DP. Interestingly, the edge states of graphene nanoribbons induced by 2D topological DP and CP exhibit out-of-plane atomic vibrations and in-plane circularly polarized atomic vibrations, respectively. This model provides deeper insight into topological phonons in graphene and a wide range of 2D materials, promising low-dissipation thermal transport and robust phononic devices.