Helical edge states and topological phase transitions in phononic systems using bi-layered lattices

摘要: We propose a framework to realize helical edge states in phononic systems using two identical lattices with interlayer couplings between them. A methodology is presented systematically transform quantum mechanical lattice which exhibits lattice, thereby developing family of states. Parameter spaces topological phase boundaries the vicinity transformed system are illustrated demonstrate robustness imperfections. potential realization terms fundamental building blocks for hexagonal and Lieb lattices. The composed passive components set disks linear springs. Furthermore, by varying spring stiffness, transitions observed, illustrating tunability our