The Research On Double Dirac Point And Its Topological Properties In Elastic Shear Waves

Recently,double Dirac cone and its properties,in optical wave system?acoustic wave system even in elastic wave system,have been aroused widely attention between humans.Numerous interesting and valuable phenomena have been discovered,such as pseudospins?topological edge states and robust one-way propagation and so on.Therefore,crystals with double Dirac cone are expected in diverse fields such as wave manipulation and energy flow control.In this dissertation,we have designed a new two dimentional?2D?phononic crystals?PCs?,from which we obtained a double Dirac cone at the center of Brillouin zone?BZ?,and also we have studied its physical properties.A simple 2D PCs consisting of a triangular array of core-shell cylinders embedded in an epoxy background has been designed,and the core is iron,while the shell is rubber.We utilize the high spatial symmetry between the crystal lattice and the scatters to create double Dirac cone.In the paper,we present a study on the scientific problems including physical mechanism and application associated with the double Dirac cone dispersions induced by two 2D accidental degeneracy.Through calculating effective Hamiltonian and Chern number combined with finite element simulation,we deeply and systemically studied the double Dirac cone in elastic wave.The research work and the results are as followed:1.By altering the geometrical parameters of the cylinders,we discover that a double Dirac cone appears at the center of BZ and the band around?point is linear.If we continue tuning the geometrical parameters,we can see band gaps and band inversion between E₁ and E₂eigenstates achieved at the BZ center,which signifines a topological phase transition from a trivial PC to a nontrivial PC.2.Based on k.p perturbation method in quantum system,an effective Hamiltonian is developed to characterize the topology of the PC around the?point,and spin Chern numbers are identified as the appropriate topological invariant.Helical edge states are formed at the interface between topologically distinct PCs,and these edge modes exhibit interesting one-way propagation behaviors with little backscattering.3.With full-wave simulations,we unambiguously demonstrate the robustness of the edge states against different types of defects,which is due to the nontrivial topology of the system.These unidirectional and robust transport phenomena of elastic shear wave thus offer people a new degree of freedom to control and manipulating elastic waves and are expected to find potential applications in diverse fields.