A Research On Edge Propagation Characteristics Of Two-dimensional Phononic Crystals

In recent ten years,phononic crystals and acoustic metamaterials have attracted wide attention due to their rich scientific connotation,peculiar physical properties and potential application prospects.Many of their properties,such as negative refraction,sub-wavelength imaging and strong reflection,completely overturn people's understanding of the physical properties of traditional materials.In condensed matter physics,topologically protected edge transportation makes the study of topological edge states of two-dimensional acoustic systems a hot topic in phononic crystals.Thus far,the topological edge states of phononic crystals are mainly based on the band structure generated by Bragg scattering,which is generated by the opening of Dirac cones fixed at the high-symmetry points of the Brillouin zone.It is difficult to realize the topologically protected one-way edge transmission of low frequency acoustic waves.In this paper,we propose a simple two-dimensional square lattice phononic crystal.We systematically study the relationship between Dirac cones fixed at the high-symmetry lines the of the Brillouin zone boundary and the symmetry of phononic crystal.The Dirac cones can be unbuckled and a complete band gap can be induced through breaking the mirror symmetry.Interestingly,by simply rotating the phononic crystals,we obtain the valleylike edge states and explore the edge transmission characteristics.Finally,we construct a space-coiling acoustic metamaterial to realize the sub-wavelength topological valley spin edge transmission.The paper includes the following main research contents:?1?In order to study the relationship between Dirac cones fixed at the high-symmetry lines of the Brillouin zone boundary and mirror symmetry of two-dimensional phononic crystals in square lattice,we design C_4v symmetrical phononic crystals,C_2v symmetrical phononic crystals,C_s symmetrical phononic crystals and C₄symmetrical phononic crystals.We calculate two-dimensional band structure and three-dimensional band structure of phononic crystal primitive cells by finite element analysis software.We find that the formation of Dirac cones fixed at the high-symmetry lines of the first Brillouin zone is caused by mirror symmetry.By changing the filling rate in a certain range,we find that the Dirac cones move steadily along the high-symmetry lines of the Brillouin zone boundary,which means that the Dirac cones fixed at the high-symmetry lines of the Brillouin zone boundary are protected by mirror symmetry.?2?In this paper,a special valleylike edge state is realized by using a simple two-dimensional phononic crystal in square lattice.The emergence of such Dirac cones,characterized by the vortex structure in a momentum space,is attributed to the unavoidable band crossing protected by the mirror symmetry.The Dirac cones can be unbuckled and a complete band gap can be induced through breaking the mirror symmetry.By continuously changing the rotation angle of phononic crystals from-45to 45 degrees,the valleylike vortex and the energy band inversion effect are realized,which leads to the valley Hall phase transition.Along the valleylike PnC interfaces separating two distinct acoustic valley Hall phases,the valleylike protected edge transport of sound in domain walls is observed in both the simulations and the experiments.?3?In this paper,by introducing the space-coiling structure,a space-coiling phononic metamaterial with C_3v symmetry is designed.At the K?K'?points of the Brillouin zone,the bands linearly cross to a subwavelength Dirac degenerated cones.With a rotation of the acoustic metamaterials,the mirror symmetry will be broken and the Dirac degenerated cones will be reopened,leading to subwavelength topological phase transition and subwavelength topological valley-spin states.Lastly,along the topological interface between acoustic metamaterials with different topological valley-spin states,we successfully observe the phononic topologically valley-spin transmission.In this paper,we improve the theoretical framework of the phononic crystal Dirac cones,provides theoretical support for judging the Dirac cones fixed at the high-symmetry lines of the the Brillouin zone boundary of phononic crystal by using the point group symmetry.These results are promising for the exploration of alternative topological phenomena in the valleylike phononic crystals beyond the graphenelike lattice.The subwavelength Dirac conical dispersion and the subwavelength topological valley-spin state breakthrough the limitation of the geometric dimension of the phononic topological insulator,and provide a theoretical basis for the application of the phononic topologically robust transmission in low frequency.