Quadratic Dirac Point And Quadratic Nodal-line Semimetal In Phononic Crystals

Sound wave manipulation plays an increasingly important role in modern production and life.In addition to the traditional vibration and noise control of daily life,many fields,such as national defense industry,biomedicine and environmental monitoring,have put forward new requirements for the control of sound waves.Phononic crystals are artificial structural materials whose mass density and elastic parameters are periodically arranged in space,and they have unique acoustic properties beyond natural materials.Therefore,phononic crystals provide new ideas and methods for manipulating the propagation of sound waves.Inspired by the study of topological states in electronic systems,recently,the study of topological states in acoustic systems has attracted widespread attention.Phononic crystal is a macroscopic system with the advantages of strong maneuverability,easy sample preparation and experimental measurement,making it an ideal platform for discovering new topological states and topological transport phenomena.With the realizations of acoustic Weyl and Dirac semimetals,various types of point or line degenerate semimetals have also been achieved in phononic crystals,and related novel transport phenomena have also been observed.In addition to the basic research value of the topological states in phononic crystals,they have practical application value for the development of low-loss acoustic communication devices.What's more,they also have great potentials in acoustic signal detection and control.This thesis mainly studies the topological states and transport behaviors in the bilayer and multilayer phononic crystals of honeycomb lattices,connected by cavities and rods.The specific research contents are as follows:In Chapter 3,we build a two-dimensional phononic crystal with a bilayer ABstacked graphene structure,which possesses a pair of quadratic Dirac points,and realize the valley topological phase and related topological transport.Similar to the AB-stacked bilayer graphene,the quadratic Dirac point hosts a 2? Berry phase at the high symmetry point K(or K').In order to further study the topological characteristics of the bilayer system,we adjust the height of the acoustic cavities to break the inversion symmetry,so that the quadratic Dirac points open bulk gaps,and two valleys at points K and K' are created with±1 valley Chern numbers.According to the bulkboundary correspondence,edge states exist at the zigzag boundary of a single valley phase,and also appear at the domain wall between two distinct valley phases,regardless of the zigzag or armchair boundary.In Chapter 4,we constructed a phononic crystal semimetal with quadratic nodalline degeneracy by stacking the AB-stacked hexagonal bilayer structure along the z direction.The topologically protected drumhead surface states are observed on the boundary of the phononic crystal.C3v symmetry and mirror symmetry guarantee the existence of the nodal-line degeneracy.The 2? Zak phase,obtained by integrating the Berry connection around the nodal-line,ensures the surface states with four-fold degeneracy.Due to the flat dispersion of the surface state,it is also called drumhead state.