A Research On Elastic And Acoustic Higher-order Topological Insulators In Phononic Crystals

In traditional integrated devices,due to the inevitable defects and impurities in the processing,a large amount of scattering and loss of wave energy are induced during the transmission process.As a result,the application and development of high-performance integrated optical and acoustic devices,such as sensors and so on,is restricted.Topological insulators in phononic crystal,especially higher-order topological insulators(HOTIs)determined by bulk polarization in the past five years,provide solutions for overcoming this difficulty due to their unique lossless transmission characteristics and defect immunities.However,as dispersion relationship of elastic waves are more complex,the research on HOTIs in elastic waves is not as deep as in light / acoustic waves.At present,the two-dimensional elastic structures that can achieve HOTIs are mostly very complicated,which is not conducive to processing and manufacturing and subsequent practical application scenarios.In this paper,based on the nearest-neighbor couplings mechanism and the pseudospin-valley-coupled mechanism,two kinds of two-dimensional elastic phononic crystal plates with simple structures are proposed respectively.Those lead to the first implementation of HOTIs in simple two-dimensional continuous elastic systems.Then,with the use of a structure similar to the Helmholtz resonator,the acoustic HOTI is extended to the threedimensional field at a scale close to the sub-wavelength.As a result,the limitations of the two-dimensional structure are broken.The research in this paper has potential application prospects in elastic wave and acoustic wave energy recovery and high precision acoustic sensors.This paper includes the following main research contents:(1)Based on the nearest-neighbor couplings mechanism,a simple twodimensional elastic phononic crystal plate with higher-order topological states is designed.By calculating the band structures of shrunk supercell and expanded supercell,we can draw the conclusion that the elastic phononic crystal plate with shrunk composite cells is topological nontrivial and the one with expanded composite cells is trivial.By constructing phononic crystal plates of hexagon-shaped,triangle-shaped and parallelogram-shaped,we can observe the distribution of one-dimensional gapped edge states,zero-dimensional topological corner states and zero-dimensional trivial corner states.Moreover,the topological corner states and the trivial corner states can be distinguished by artificially constructing the defects.The results show that the topologically protected corner states only appear at obtuse angles,not at acute angles.Finally,the concept of topological index is introduced to theoretically explain the relationship between the topologically protected corner states and the angle of the corners.All the simulation results are verified by experiments.Previously,the realization of higher-order topological states of elastic waves required very complex structures based on tight-binding model of positive and negative coupling.In this paper,we can break the limitation and greatly simplify the design difficulty.(2)Based on the pseudospin-valley-coupled mechanism,a two-dimensional elastic HOTI is proposed.Pseudospin-orbit coupling gapless edge states and valley-polarized gapless edge state are respectively induced by the lattice deformation and the mirrorreflection symmetry breaking.When the lattice deformation and the mirror-reflection symmetry breaking are introduced simultaneously,the topological gapless edge states evolve to be gapped and the topological corner state emerges.Four pseudospin-valleycoupled composite cells are stitched together to form a complete structure of elastic phononic crystal plates with gapped edge states and topologically protected corner state.The presence of the first-order gapped edge states and the second-order topological corner state is proved experimentally.(3)This paper proposes a three-dimensional acoustic metamaterial with first-order surface states and second-order hinge states.The unit cell structure is similar to the Helmholtz resonator,which can be used to realize three-dimensional acoustic HOTIs on the scale close to sub-wavelength.The intra-cell and inter-cell coupling strength can be changed by adjusting the radii of the intra-cell and inter-cell connecting pipes.By calculating the energy band structures of the supercells and the eigenfrequencies and transmission spectra of the three-dimensional acoustic metamaterials,we can draw the conclusion that: when the intra-cell coupling strength is less than the inter-cell coupling strength,there are second-order hinge states and first-order surface states in the complete bandgap range;when the inter-cell coupling strength is less than the intra-cell coupling strength,the acoustic wave will not propagate in any part of the acoustic metamaterial in the complete bandgap range and the acoustic metamaterial is trivial.This research makes up for the lack of research on HOTI in two-dimensional elastic structures,and implements HOTIs in two-dimensional continuous elastic systems with simpler structures.As a result,the design difficulty is simplified.What's more,the use of two different mechanisms to achieve elastic HOTIs increases the possibility of design.Finally,the realization of HOTI in three-dimensional acoustic metamaterial expands the scope of research,and provides a theoretical basis for acoustic wave control in three-dimensional structures at sub-wavelength scales.