Researches On Topological Characteristics Of Two-dimensional Phononic Crystals

Since M.Kushwaha proposed the concept of phononic crystal(PC)in 1993,the PCs have received extensive attention and research.The PCs can be designed and adjusted flexibly,and their energy band dispersion relationship can be flexibly regulated for a variety of functional designs.Therefore,the PCs have been rapidly developed and widely used in the regulation of acoustic wave and elastic wave and acoustic devices,such as the self-collimation,negative refraction,focusing,rectification and so forth.In recent decades,the study of the topological insulators and related topological properties of electronic systems has become a hot topic in the field of condensed matter physics.In 2016,three scientists,Thouless,Haldane and Kosterlitz,jointly won the 2016 Nobel Prize for physics for their outstanding contributions to the study of the topological phase and topological phase transitions,which also greatly inspired other researchers in this field.The unique electrical transport properties of topological insulators have many potential applications in spintronics,thermoelectrics and quantum computing.Due to the similarity of the band theory in the periodic structures,the concept of topology was successfully extended to the Bose systems,including the photonic crystals and the PCs.Actually,this not only provides a wealth of new physical content for optics and acoustics,but also offersmore possible ways for the regulation of classical waves.The topological phenomena in the acoustics system have attracted a lot of attention because of their peculiar physical properties and attractive application prospects.In recent years,some important research results have been achieved,such as the successful implementation of the acoustic quantum Hall effect,acoustic quantum spin Hall effect and acoustic valley Hall effect.In the theoretical and experimental research of the topological acoustics,the PCs provide an excellent research platform due to their adjustable characteristics.The transmission of the topologically protected edge states in PCs has the characteristics of backscattering suppression and robustness against defects and disorders.Therefore,the topologically protected edge states has great application prospects in acoustic communication,noise control,and acoustic and electrical integration.In this thesis,we have done some research on the topological characteristics of two-dimensional phononic crystals,including the starting point of the topological phenomenon in the PCs--Dirac degeneracy,acoustic topological phase transition and pseudomagnetic field in the PCs.The main works are listed below:1.The accidental Dirac degeneracy and topological phase transitions in the PCsWe studied the accidental Dirac degeneracy ’appearing in the corner and center points of the hexagonal Brillouin zone of the PC,and the acoustic topological phase transition resulted from the breaking of the Dirac degeneracy.Using the orientation degree of freedom of the scatterers,we realized the accidental Dirac degenerate at the corners of the Brillouin zone of the PC with C3 symmetry.Once opening the energy gap near the Dirac degenerated point,the order of the frequency bands was interchanged,so we achieved the topological valley Hall phase transition in the PC.We also observed a time-reversal pair of edge states within the interfaces between two PCs with different topological phases,and the topologically nontrivial edge states could propagate along a zigzag bending channel with high transmission rate.We also applied this method to the PC with C6 symmetric to produce an accidental double Dirac degeneracy at the center of the Brillouin zone.Similarly,the opening of the energy gap near the double Dirac degenerated point by rotating the scatterers resulted in the occurrence of the acoustic quantum spin Hall transition in the PC.2.Experimental observation of pseudomagnetic field and Landau level in phononic crystalsBy altering the aspect ratio of the elliptical scatterers in a PC,we designed a two-dimensional gradient PC with spatial dependent gauge field.Taking advantage of the gauge field,we constructed a uniform pseudomagnetic field in the PC and achieved the acoustic quantum Hall effect.Under the pseudomagnetic field,discrete relativistic Landau energy levels with plateau related to high degenerated states appeared in the two valleys of the PC’s band structure.In our experiments,we have observed several peaks of the total energy spectrum corresponding to the Landau levels of the PC,and the experimental measurement results are consistent with the simulation results and the theoretical calculation results.In addition,we observe experimentally that the states on the n=0 Landau platform have the characteristics of sublattice polarization,whose eigen-mode fields are completely localized on the q-sublattice.The states between two discrete Landau levels correspond to the edge states which localize on the physical boundary of the PCs.Therefore,when we placed a source near the boundary of the PCs in the experiment set-up,we can successfully excite the edge state with the corresponding frequency.