Study On Acoustic Topological Heterostructures And Type-Ⅱ Acoustic Semimetals

In recent years,topological physics has been extended from electronic systems to macroscopic artificial acoustic structures,where a series of interesting acoustic phenomena have been discovered.These topological acoustic structures include acoustic metamaterials,acoustic metasurfaces and phononic crystals.The acoustic wave equation,for its scalar wave nature,is similar to the Schr?dinger equation.Compared with electronic systems,phononic crystals have the advantages of simplicity,stability,macroscopic and safety,which facilitate further explorations for novel physical phenomena in practical systems and potential acoustic applications with topological protection.In this thesis,we systematically investigate the topologically relevant acoustic transport phenomena in two-dimensional and three-dimensional topological phononic crystals,including robust transport in topological heterostructures based on two-dimensional acoustic topological insulators,the Lifshitz transitions in three-dimensional acoustic Dirac semimetals,and three-dimensional acoustic type-Ⅱ triply degenerate semimetals and defect-immune chiral surface states.The following is a brief introduction:1.Robust acoustic waveguide transports in heterostructures based on acoustic topological insulatorsBased on the acoustic topological insulators with pseudospin,we theoretically predict and experimentally observe topological heterostructures that host a pair of helical waveguide modes.Different from the one-dimensional topological boundary states,with the freedom of width,the waveguide modes are of adjustable capacity of transmissions,and convenient for applications.We demonstrate the partition and beam collimation of the topological waveguide modes.The collimated sound beam depends on the thickness of the middle layer of the heterostructures.Furthermore,we verify the robust transmission properties of the topological waveguide states in the heterostructures,which are immune to disorders and structural defects.These results pave a way to explore the topological transports in versatile designs of heterostructures for acoustic waves.2.Topological Lifshitz transition in 3D acoustic Dirac semimetalWe theoretically predict topological Lifshitz transitions in acoustic Dirac semimetals.Combining the tight-binding method and the finite-element method,we find that the phononic crystal undergoes a topological Lifshitz transition when the radius of the scatterer is changed,that is,it transits from the three-dimensional type-Ⅱ Dirac semimetal with N=1 to the three-dimensional half-type Dirac semimetal with N=0.As the scatterer radius decrease,the phononic crystal further undergoes a metalinsulator phase transition,that is,from a three-dimensional half-type Dirac semimetal phase with N=0 to the three-dimensional atomic insulator with N=0.We have analyzed the equi-frequency dispersion near the acoustic Dirac point,and calculated the topological charge of the two Dirac semimetal via the non-Abelian Berry phase,thus confirming the acoustic Lifshitz transition.We also calculate the surface states of the two kinds of three-dimensional acoustic Dirac semimetals and find that both of them possess helical topological surface state with pseudospin-momentum locking.3.3D Acoustic type-Ⅱ triple degenerate semimetalWe theoretically predict three-dimensional acoustic type-Ⅱ triply degenerate semimetals.We find that the acoustic type-Ⅱ triply degenerate semimetal has three different types of triply degenerate points.By numerical simulation,we find that the frequency and positions of these triply degeneracy points will move in momentum space when changing the scatterer radius.Finally,we find that three-dimensional acoustic type-Ⅱ triply degenerate semimetal has defect-immune surface states.