Ultra-broadband edge-state pair for zigzag-interfaced valley Hall insulators

The existence of a single topologically protected edge state in the first bulk bandgap for acoustic/elastic valley Hall insulators (VHIs) with zigzag interface configurations (ZICs) is well known. However, in this work, we show that an ultra-broadband edge-state pair in this bandgap can be created using the inverse design by topology optimization. The valley Hall insulator design increases the operational bandwidth 121% compared with an existing valley Hall insulator from recent literature and exhibits extreme field confinement, where more than 99% of the field intensity is concentrated within three unit-cells from the interface. One-way propagation and topological robustness towards small cavity defects are confirmed for the full bandwidth. The exploitation of such edge-state pairs of valley Hall insulators opens an avenue for realizing broadband confined edge modes. In tests for disorder and bend defects, we show that the additional ZIC, with a different operational frequency interval, encountered at the defects, degrades the transmission for bend and disorder defects which may prove significant for the application of VHIs. Through an alternative topology optimization method based on two ZICs, we further increase their common operational bandwidth.