Robust Edge States Of Two-dimensional Phononic Crystals Beyond High-symmetry Points Of Brillouin Zones

Sound wave is a kind of vibrating mechanical wave,and its control plays an increasingly important role in modern production and life or other aspects.In addition to the traditional vibration and noise control in daily production and life,the emerging fields such as environmental monitoring,national defense industry,biochemical analysis,disease inspection and health monitoring have put forward new requirements for sound wave control.In the field of sonic control,the strong edge states of phononic crystal system with Dirac point fixed at the corner or center of Brillouin zone have received widespread attention.The discovery of topologically protected edge states of phononic crystals has made the study of topological edge states of Two-dimensional acoustic crystal systems a hot topic in the field of topological materials.Phononic crystals have unique band gaps and acoustic edge transmission characteristics,which provide new research methods for the artificial manipulation of mechanical wave propagation in elastic media and structures.This paper systematically studies the relationship between the Dirac point on the highly symmetrical boundary of the Brillouin zone of a Two-dimensional phononic crystal and the mirror symmetry of the phononic crystal.The rotation of the scatterer opens the Dirac point on the highly symmetrical boundary to obtain the valley-like edge State,the edge transmission characteristics of the Two-dimensional phononic crystal system are explored.The transmission characteristics of the topological edge states of the phononic crystal system such as lossless transmission,and robustness of backscatter suppression provide new research ideas for the exploration of various new acoustic functional products.The paper includes the following main research contents:(1)In this paper,the mechanism of Dirac dispersion is discussed systematically from the angles of square lattice,rectangular lattice,central rectangular lattice and triangular lattice,and the energy band degeneration of two-dimensional phononic crystals in different plane lattices is studied.Due to the energy band crossing in the presence of mirror symmetry of the two-dimensional phononic crystal,the degenerate points of these energy band structures have the characteristics of vortex structures in momentum space.In the process of opening and closing the forbidden band of the energy band structure,when the mirror symmetry of the phononic crystal is not destroyed,then the Dirac point due to the inevitable degeneration of the energy band structure is stable.Changes in the geometric parameters of the scatterers can change the position of these Dirac points on the Brillouin zone,but they cannot be eliminated.(2)In this paper,by rotating the scatterer to break the mirror symmetry of the two-dimensional phononic crystal,the corresponding Dirac point will be opened,resulting in a directional or complete energy band gap.The band gap of the phononic crystal can effectively prevent the propagation of sound waves in the phononic crystal system.When the anisotropic scatterer of the phononic crystal rotates from left to right or from right to left,it is accompanied by the Dirac point energy band The opening-closing-reopening of the gap proves that the Dirac point of the two-dimensional phononic crystal can degenerate at the high symmetric boundary of the first irreducible Brillouin zone.Similar to the valley coupling,the reversal of the energy band of the phononic crystal leads to a topological phase change,and an edge state is generated along the interface between two phononic crystals with opposite topological phases.(3)In this paper,a phononic crystal system with a plane group of P3m1 is designed,and the supercell band gap characteristics and acoustic edge propagation characteristics of its linear and zigzag interfaces are analyzed by simulation,and their effects on the cavity,disorder or bending are experimentally studied.The valley-like edge states of phononic crystals with crystal plane group P3m1 have been clearly verified and determined.This paper systematically reveals the relationship between the Dirac point changing along the boundary of the Brillouin zone and the planar crystal group,and provides a method to induce the robust edge states of phononic crystals in various planar lattices.Simultaneously,this paper expands the theoretical framework of the Dirac cone on the highly symmetric boundary of the two-dimensional phononic crystal,broadens the research scope of various sound propagation phenomena of the two-dimensional phononic crystal,and is also conducive to exploring new topological insulators.On the one hand,the theoretical framework of Dirac point system of two-dimensional phononic crystal is further improved by studying the Dirac point system with high symmetry boundary in Brillouin zone of two-dimensional phononic crystal.On the other hand,it provides knowledge reserve for judging the Dirac point system of phononic crystal by point group symmetry,and offers a technical scheme to study the acoustic propagation characteristics of the phononic crystal Dirac point system.