Study On The Topological Properties Of Bilayers Acoustic Crystals

Topological insulators are important research objects in condensed matter physics.In the field of topology,important achievements have been made in electromagnetic wave,acoustic wave,elastic wave and water wave systems,such as the edge states of spin locking and the characteristics of immune deficiency.The quantum spin hall effect in classical waves is realized by constructing pseudo-spin degrees of freedom.For the quantum valley hall effect,it is realized by the unequal energy valley degrees of freedom in the momentum space.The quantum spin hall effect and quantum valley hall effect have been widely studied in artificial metamaterials such as photonic crystals and acoustic crystals because they can be realized by just breaking the symmetries of the structure.In this paper,we studied about the robust transport of acoustic edge state signals along interfaces between distinct topological phases.The research work and the results are as followed:1.First,we construct a bilayers acoustic crystal with honeycomb lattice of connected cavities.There are four cavities and four connected wave guides.We realized the degenerate state by adjusting parameters.Due to the coupling between upper and lower layers,a diamond ring is formed at K.Then by breaking the mirror symmetry along the z axis and the inversion symmetry in the plane,the diamond ring is pulled apart and form the quantum spin hall effect and quantum valley hall effect which are similiar to the electronic system.The Hamiltonian and the Chern number of each system are written out to determine the topological phase of the system,and the phase distribution diagram is also drawn to obtain the topological phase transition boundary.2.Then we study about the edge states.As we all known,the interface between two kinds of acoustic crystals with different topological properties can produce topological edge states.Here,We studied three edge states: the interface between different quantum spin topological phases,the interface between different quantum valley topological phases and the interface between quantum spin topological phase and quantum valley topological phase.In the quantum spin topological system,there are two intersecting edge states,and the sound pressure is distributed either in the upper layer or the lower layer,which is induced by layer pseudo-spin.In the quantum valley topological system,there will be two edge states with the same bending direction,K and K?have different spins.In the mixed system,only one edge state appears,the K locks spin-down state and the K?locks spin-up state.3.At last,we simulate the application of the acoustic crystal.We designed three different acoustic crystal devices,of whose interfaces consist of different topological phases.In the first simulator,through the spin locking and valley degree of freedom,we realized the directional transport of sound signal along the preferred paths.In the second device,since the wave source is allowed to carry both spin and valley information in each transmission channel,by selective placement of the wave source and selective excitation of edge state to the wave source,we realized a multi-port valve for power distribution and feeding.In the third device,the asymmetric transmission of the edge state is realized by designing the left and right asymmetric acoustic crystal structure.