Coupled topological edge and corner states in two-dimensional phononic heterostructures with nonsymmorphic symmetries

Abstract

Abstract The exciting discovery of topological phononic states has aroused great interest in the field of acoustic wave control. However, conventional topological edge states and corner states localized at the interface and corner of the two-phase domain wall structures are limited by single channel transmission characteristics, which decreases the flexibility of designing multi-channel acoustic wave devices. Here, we propose a two-dimensional (2D) topological phononic heterostructure with nonsymmorphic symmetries to realize the multiple interface topological multimode interference effect based on the coupling of topological edge and corner states. Topological phase transitions are achieved by altering the rotation angle of the split-ring scatterers in a square lattice. The coupled edge states are generated by the coupling between the edge states of ordinary-topological-ordinary (OTO) interfaces. Moreover, the higher-order topology of the square phononic crystals (PCs) is characterized by nontrivial bulk polarization, the topological and coupled corner states splitting into two pairs appear in the square OTO bend structure owing to the nonsymmorphic PC lack of mirror symmetries. Finally, the topological robustness of the multimode interference effect of coupled edge and corner states against defects is demonstrated. Our results pave the way for guiding and trapping acoustic waves in topological nonsymmorphic heterostructures, whose multi-channel transmission capability can be employed for designing topological phononic filters, couplers and multiplexers.