Theoretical And Experimental Study Of Topological Edge State Propagation In Phononic Crystals

Acoustic control plays an increasingly important role in modern production,life and other aspects.In addition to the traditional vibration and noise control in daily life and production,the new cross-cutting fields of national defense industry,environmental monitoring,biological analysis,early diagnosis of diseases and health monitoring have put forward new requirements for sound control.Phononic crystals have unique band gap characteristics,which provides a new method for manipulating wave propagation in elastic media and structures.The characteristics of phononic crystals,such as lossless transmission of topological boundary states,one-way sound transport and robustness of backscattering-immune wave transport,provide new ideas for the exploration of new acoustic functional devices.With the rapid development of two-dimensional acoustic system topological edge state research,acoustic topological insulators have become a research hotspot in the field of phononic crystals,and researchers also started to study three-dimensional acoustic topological surface states.On the whole,the study of the topological edge states of three-dimensional phononic crystals is still in its infancy.Based on the research of two-dimensional acoustic topological insulator,a simple operation of rotating triangular column is constructed to realize phononic crystal topological insulator.The simulation and experiment show that the phononic crystal can achieve robust one-way sound propagation.On the basis of the two-dimensional study,a three-dimensional woodpile chiral interlayer coupled phononic crystal is constructed.The topologically protected one-way propagation of acoustic waves in its nontrivial gaps is verified by simulation and experiment.The main research work is as follows:（1）We design a two-dimensional phonon topological insulator and analyze its band structures.By introducing a zone folding mechanism,we realize the topological phase transition in a double Dirac cone of the rotatable triangular phononic crystal with C_3v symmetry.According to the common influencing factors of Dirac point,the influence of filling ratio and symmetry on the double Dirac point is discussed.The results show that filling ratio does not affect the opening and closing of the double Dirac point.The symmetry of the double Dirac point is reduced by rotating triangular column,which leads to the opening of the Dirac point.On the two-dimensional plane,linear and zigzag interfaces are constructed,and the differences of band gaps between different interfaces are compared.The difference provides theoretical support for the edge state at different interfaces.（2）We validate the topological states of phononic crystals backscattering-immune in one direction.The characteristics of different boundary modes of linear and zigzag interfaces are compared in detail.The pseudo-spin propagation of zigzag interfaces is verified by experiments.To verify the robust transport of our topological phononic insulator,we provide different defects,such as cavities and disorders.Based on different topological phases,we set different propagation paths.We design a simple two-point propagation path and more complex asteroid pathway and HNU path to realize robust reconfigurable transport property.（3）We systematically investigate the relationship between the Weyl points and the screw symmetries.We design and fabricate a 3D acoustic semimetal composed of rotationally stacked rods with 6₂ screw symmetry.This acoustic semimetal not only possesses a linear Weyl degeneracy with a charge of 1（or-1）,but also has a double Weyl point with a charge of 2（or-2）.When the screw symmetry of this acoustic semimetal is reduced from 6₂ to 2₁,we found that double Weyl point split into a pair of Type-I（or Type-II）single Weyl points.When the screw symmetry is increased from6₂ to 6₃,both the linear and double Weyl points are always degenerated at the k_z direction without gaps.（4）We validate the surface states related with Weyl points inside the nontrivial gaps.Firstly,the surface states of screw symmetry 6₂,6₃ and 2₁ are analyzed,and the surface modes in the nontrivial gaps are analyzed in detail.Secondly,for screw symmetry 6₂,the topologically protected one-way propagation of acoustic waves is simulated by choosing different k_z values.Defects such as cavities and bending are set to verify the one-way propagation of surface states.The transient analysis of the acoustic wave packet at different times also verifies non-reciprocally counterclockwise propagation.Finally,the experimental verification is carried out,and the one-way propagation of the surface state are verified by measuring the surface acoustic pressure of the experimental samples.Due to their good fabricability and topological non-reciprocity,these acoustic semimetals provide potential platforms for noise processing,acoustic signal processing,and surface acoustic wave devices.