Topological insulator in a hexagonal plate with droplet holes

In this study, we introduce a tunable topological insulator (TI) system consisting of a hexagonal aluminum plate with rotatable droplet-shaped holes to produce topologically protected edge waves (TPEWs) along a topological interface. By rotating the round plate in the unit cells to break the unit cells' mirror symmetry while preserving C3 symmetry, a new band gap is produced from the dispersion relations' Dirac point. A topological protection state is generated at the interface due to the valley Hall effect. We also simulate different TPEWs along disparate interface routes and further prove their robustness, which means that they are immune to the vast majority of backscattering along interfaces. We also demonstrate that TPEWs at specific frequencies can be transported to different locations in hexagonal TIs, which is an innovative technique for precise control of acoustic guidance. This study provides a new method to modulate guide waves and energy accumulation of different frequency waves in topological systems.