Research On Topological Boundary States In Two-Dimensional Acoustic Artificial Structures

In recent years,topological insulators have become a major research focus in condensed matter physics.Topological insulators are characterized by internal insulation,but there are propagating or localized boundary states on their boundaries.The topological protection of this boundary state receptor has the characteristics of anti-disorder and suppression of backscattering,and is called topological boundary state.According to different bulk-edge correspondences,topological insulators can be divided into traditional（first-order）topological insulators and higher-order topological insulators,which have first-order and higher-order topological boundary states,respectively.Higher-order topological insulators are a new class of topological insulators discovered in recent years,which have been realized in various classical wave systems such as optics and acoustics.In this context,this paper studies first-order and higher-order topological boundary states in acoustic artificial structures,respectively:an acoustic metamaterial designed using Mie resonant elements realizes first-order topological boundary states and verifies its robustness;design a simple two-dimensional acoustic lattice realizes second-order topological boundary states,namely topological corner states.In addition,its application is explored based on second-order topological phononic crystals,and topological beam splitting is realized and its superiority is demonstrated.In the 2nd chapter,an acoustic four-channel square Mie resonator element is designed,which contains structural features of subwavelength size,and its equivalent model can be regarded as a combination of an ultra-slow acoustic medium with higher refractive index and a rigid frame material.An acoustic metamaterial with a topological phase transition is constructed,in which the energy bands are inverted as the system parameters change,resulting in a Zak phase transition.The Zak phase describes the topological properties of energy bands in a one-dimensional periodic system,and the properties of topological boundary states can be predicted according to the body-edge correspondence.Further investigations reveal that the topological boundary states realized by the subwavelength structure are robust to disorder and waveguide bending.In the 3rd chapter,a two-dimensional acoustic honeycomb structure with triangle resonant cavity is numerically studied.Topological phase transition is induced by gradually adjusting the intracell and intercell coupling,and then the topological phase is used to construct a second-order topological insulator.The topological properties of second-order topological insulators can be characterized by quantized quadrupole moments.When quantized quadrupoleQ_ij 0,the system is trivial;whileQ_ij1/2,the system is topological nontrivial.We investigate the acoustical higher-order states of triangular and hexagonal structures,respectively.Topological corner states were observed in both structures.The robustness of the corner states against disorders was also demonstrated.The topological corner modes will offer a new route to robustly confine sound in compact acoustic systems.In the 4th chapter,a two-dimensional tetragonal phononic crystal is theoretically proposed in which the acoustic band gap and band topological properties can be controlled by rotating elliptical scatterers in a unit cell.The quantum spin Hall effect is simulated in the bulk band gap of a two-dimensional phononic crystal,resulting in a one-dimensional helical boundary state.Due to the breaking of spatial symmetry,a boundary state with a band gap will be generated,thereby realizing a zero-dimensional topological corner state within the band gap of the boundary state.Using the symmetric eigenvalues of the acoustic Bloch wave function,the underlying topological mechanism is revealed.Furthermore,topological beam-splitting effects are found in gapless boundary states,which provide a new way to control acoustic transport in higher-order systems and provide a new way for the design of acoustic directional antennas.