Topologically Invisible Defects in Chiral Mirror Lattices

One of the hallmark of topological insulators is having conductivity properties that are unaffected by the possible presence of defects. In this work, by going beyond backscattering immunity and topological invisibility across defects or disorder is obtained. Using a combination of chiral and mirror symmetry, the transmission coefficient is guaranteed to be unity. Importantly, but no phase shift is induced making the defect completely invisible. Many lattices possess the chiral-mirror symmetry, and the principle is chosen to be demonstrated on an hexagonal lattice model with Kekulé distortion displaying topological edge waves, and analytically and numerically is shown that the transmission across symmetry preserving defects is unity. Then this lattice in an acoustic system is realized, and the invisibility is confirmed with numerical experiments. It is foreseen that the versatility of the model will trigger new experiments to observe topological invisibility in various wave systems, such as photonics, cold atoms or elastic waves.