Valley Topological Transport And Nodal Line In Two-Dimensional Phononic Crystals

The phononic crystals(PCs)is composite artificial materials whose mass density and elastic parameters are periodically arranged in space.Using the band structure of the sound wave in PCs,the control of the sound wave can be realized,and a novel acoustic effect can be obtained.For example,the PCs are used to realize acoustic negative refraction,superlens,orientation,collimation,one-way transmission and Bloch oscillation and so on.In recent years,the concept of topology has been introduced into PCs,which has attracted great attention and formed the field of topological sound,providing a broader prospect for the development and application of PCs.Among them,as one of the representatives of the acoustic topological insulators,the acoustic valley topological insulators take valley in the momentum space as a new degree of freedom,and can generate valley-locked edge state at the interface of two different valley topological phases.They are unidirectional,which provides an effective way to achieve lossless transmission of sound waves,and has important value in applications such as acoustic devices.At the same time,the research of acoustic topological semimetals has also made great progress.For example,three-dimensional Weyl PCs and the corresponding Fermi arc surface states,three-dimensional nodal line PCs and the corresponding drumhead states have been realized experimentally.In this thesis,we studied the valley topological phases in two-dimensional single layer and bilayer PCs of a square lattice and the transport properties of the corresponding valley-locked edge states,and studied nodal line semimetal phases and the corresponding Andreev-like reflection phenomenon in two-dimensional PCs of a hexagonal lattice.The specific research content includes the following three aspects:(1)Valley topological insulators of a square lattice is realized,and the transports of topological negative refraction and abnormal partition of valley-locked edge states are observed.We constructed acoustic valley topological insulators of a square lattice by arranging two different acoustic resonators in which topological phase transition is implemented by tuning the height of two resonators.We constructed samples of straight interface and "Z" shaped interface by using different valley topological phases,and observed the topological transports of the valley-locked edge states with reflection immunity.In a sample with the interface of tilted termination,we observed the topological negative refraction phenomenon of edge states entering the outer space;since the position of the valley can move with the change of the structural parameters,the refraction angle can be adjusted accordingly.More importantly,in the designed heterostructure with four interfaces or channels,an abnormal partition phenomenon of edge states was observed at the intersection of the channels.These findings have potential value in the design and application of related acoustic devices.(2)We realized valley spin-Chern topological insulators in bilayer PCs of a square lattice.By introducing layer degrees of freedom as pseudospin,we realized valley spin-Chern topological insulators in bilayer PCs of a square lattice,whose topological invariants are valley spin-Chern numbers with the layer pseudospin.By tuning the heights of two different resonators in the upper and lower layers,four different types of valley topological phases are obtained.Taking any two different valley topological phases,we constructed three types of interfaces,and observed acoustic valley edge states of layer mixing,layer polarizing,and layer locking,respectively.In addition,we demonstrated layer-dependent partition transmission of the edge states at the intersection of the four-channel samples.By taking advantage of the additional layer pseudospin freedom,our system provides a good platform to explore intriguing transport properties of topological acoustics,and has potential application prospects in layer-dependent sound wave manipulation.(3)We designed two-dimensional nodal line PC and realized the Andreev-like reflection phenomenon of sound waves.By tuning the size and height of scatterers in a hexagonal lattice,the band with the monopole mode and the band with the dipole mode are crossed to form nodal line degeneracies,thereby realizing a two-dimensional nodal line PC.The degeneration of the nodal line is protected by the mirror symmetry in the z direction.The mirror symmetry can be broken by tilting the scatterers,so that the nodal line opens the band gap to form an insulator.The size of the band gap can be tuned by the size and shape of the scatterers.The band gap can change the modes of the incident wave and the reflected wave.For example,the incident monopole mode is reflected as a dipole mode.We constructed the nodal line semimetalinsulator interface,and found that a beam of dipole mode with retro-reflection will be generated when the incident wave of the monopole mode encounters the interface,similar to an Andreev reflection at the metal-superconductor interface.