Robust topological edge states induced by latent mirror symmetry

Abstract

In recent years, topology has offered an elegant degree of freedom (DOF) for light and sound manipulation. There exists persistent effort to explore the origin of topological phases based on symmetry, while it becomes rather challenging in complex networks or multiple DOF systems where geometric symmetries are not apparent. Here, we demonstrate a linear degeneracy induced by latent mirror symmetry in a zigzag granular chain whose DOF is three times larger than its bead number. An isospectral reduction approach and graphical representation are developed to track the topological origin of the degeneracy. We show how the latent mirror symmetry leads to the degeneracy and how it is manifested in a properly chosen eigenmode space. Moreover, we reveal the existence of topological edge states and their robustness against different disorders when the degeneracy is gapped. Our study takes a pivotal step toward exploiting topological waves in complex networks or disordered systems, opening up the perspective of offering new flexibilities for classical wave tailoring.