Phononic second-order topological phase in the C3N compound

Abstract

Second-order topological phases in artificial systems have been extensively studied, but studies in the phonons of atomic materials are limited. In this paper, we propose that phononic second-order topological phase exists in ${\mathrm{C}}_{3}\mathrm{N}$, a previously synthesized and intensively investigated two-dimensional material. Its nontrivial phase arises from the mismatch between the Wannier centers of the out-of-plane phonon modes and the atomic positions. Using a simplified force constant model, we find that gapped edge modes and in-gap corner modes only exist on the structures with broken pure-carbon-ring terminations, and this unexpected phenomenon can be explained by the electronlike filling anomaly for phonons. Further calculations reveal that these corner modes are robust to external disturbances. The nontrivial phononic phase in ${\mathrm{C}}_{3}\mathrm{N}$ provides an avenue in crystalline materials to explore higher-order topological phases in Bose systems.