Weyl Points And Associated Topological Surface States In Phononic Crystals

Weyl semimetals have great applications in the development of new electronic devices and topological quantum computing for Weyl fermions with chirality embrace numerous peculiar properties in Weyl semimetals,such as chiral anomaly and topological Fermi arc surface states.Weyl physics has recently been extended to artificial structures for classical waves,such as photonic and phononic crystals.In particular,phononic crystal samples are macroscopic,well-controlled and sound field distribution can be detected losslessly,thus it benefit us to explore the topological band physics originally proposed in electronic systems.In order to explore the physical connotation and potential application of acoustic “Weyl semimetal”.In this thesis,we have studied two types of acoustic Weyl points and associated topological surface states of charily Weyl phononic crystals.The contents including topological negative refraction of surface acoustic waves,the existence of double Weyl points and associated topological surface states,the interface state of the opposite chiral phononic crystal,and multiband acoustic focusing using labyrinthine metamaterials.The main works are listed below:1.Topological negative refraction of surface acoustic waves in a Weyl phononic crystalWe report negative refraction of topological surface waves hosted by a Weyl phononic crystal—an acoustic analogue of the recently discovered Weyl semimetals.The interfaces at which this topological negative refraction occurs are one-dimensional edges separating different facets of the crystal.By tailoring the surface terminations of the Weyl phononic crystal,constant-frequency contours of surface acoustic waves can be designed to produce negative refraction at certain interfaces,while positive refraction is realized at different interfaces within the same sample.In contrast to the more familiar behaviour of waves at interfaces,unwanted reflection can be prevented in our crystal,owing to the open nature of the constant-frequency contours,which is a hallmark of the topologically protected surface states in Weyl crystals.2.Observation of acoustic double Weyl points and associated topological surface statesWe report the experimental evidence of topological surface states in a double Weyl phononic crystal.By measuring the pressure field distribution along a vertical plane in the middle of the sample,we demonstrate the existence of the double Weyl points in the bulk bandstructure.By Fourier transforming the measured surface pressure fields,we can arrive at the dispersion surface of the surface states or the equifrequency contour(EFC)at the working frequency.Two gapless surface states exist in an nontrivial band gap and two surface arc states starts from the projection of double Weyl points end at the projection of bulk bandstruture,which implies the-2 charge of this double Weyl points.3.Topological interface states between two phononic crystal with opposite chiralityWe studied the interface states of phononic crystal structures with opposite chirality.We validate the surface states and the surface arc states at the interface of a couple of phononic crystal with opposite chirality.The edge states are localized at the interface between the right-hand phononic crystal and the left-hand phononic crystal,and support edge propagation of sound.Two gapless surface bands traverse the nontrivial band gap between the lowest two projected bulk bands.Two surface arc states at the right-hand/the left-hand phononic crystal interface starts from the projection of K,and end at the projection of H.This crystal interface holds excellent backscatteringimmune topological transport.4.Multiband acoustic focusing by graded labyrinthine metamaterialsWe present a design of gradient-index lens that can focus acoustic waves in two frequency bands.The gradient lens comprises of a series of labyrinthine metamaterials units with different length solid bars,which exhibits positive and negative relative refractive index in a classic hyperbolic secant profile at different frequencies.The effective refractive indices in each unit of the gradient lens were retrieved numerically using an inverse method.The numerical results show that the gradient-index lens allows acoustic focusing in two frequency bands,which matches well the theory.Our design offers potential application such as imaging and multifunction couplers.