Study On Weyl Points And Fermi Arc Surface States In Gyromagnetic And Chiral Metamaterials

Weyl semimetals are a new class of topological materials with linear degeneracy points(Weyl points)in three-dimensional momentum space.Weyl semimetals have unusual physical properties such as the open Fermi arc surface states and the negative magnetoresistance effects due to chiral anomaly.These properties make Weyl semimetals one of the research hotspots in the field of topological physics.In recent years,the study of Weyl points has been extended from the field of topological electronics to topological photonics with the help of well-designed photonic crystals.Compared with photonic crystals,photonic metamaterials do not have strict periodic constraints and can usually be described by homogeneous effective material parameters.The realization of Weyl points by photonic metamaterials is of great significance for the manipulation of photons and the study of photonic topological properties.In this thesis,we take the Weyl points in photonic metamaterials as the main research object.The spatial distribution of photonic Weyl points in two different symmetry-broken metamaterials is deeply discussed.We systematically study the scattering-free transport properties of Fermi arc surface states,which is essential for applications such as information multiplexing and photonic routing.The main research contents of this thesis are as follows:Firstly,in the time-reversal symmetry-broken gyromagnetic metamaterials,the three-dimensional band structure of the system is given by solving Maxwells equations.Since the frequency around the twofold degenerate point has a linear dispersion relation with the wave vectors along each direction,it is proved that there is a photonic Weyl point in the system,and the photonic Weyl point is right at the critical transition of the type-I Weyl points and the type-II Weyl points.The analytic expressions of the longitudinal mode and transverse mode forming Weyl points are deduced by the intrinsic electric field of the gyromagnetic metamaterials,and the distribution law of the number of Weyl points and their momentum space positions in the system is given.In addition,numerical calculations show the existence of Fermi arc surface states at the interface between the gyromagnetic metamaterials and vacuum,and the Fermi arc surface states connect Weyl points with opposite topological charges.The simulation results show that surface waves can propagate robustly around sharp defects,which indicates the robust transmission properties of the Fermi arc surface states.Then,the physical mechanism of Weyl point formation and the transport properties of Fermi arc surface states in chiral metamaterials with broken spatial inversion symmetry is investigated.The research shows that the chiral effect has a great influence on the band degenerate points in the double Drude materials.The double Drude materials can have two symmetrically distributed Dirac points without considering the chiral effect.When the permittivity tensor and the permeability tensor are not equal,the Dirac points in the system become the triply degenerate points,and the triply degenerate points can be regarded as the intermediate transition state of the Dirac points and the Weyl points.In the case of considering the chiral effect,the triply degenerate points can be split into pairs of Weyl points with opposite chirality,and the total number of Weyl points is an integer multiple of four.Weyl points in the chiral metamaterials are related to each other through the time-reversal symmetry.At the same time,the Fermi arc surface state generated by the Weyl points can exist in two different frequency ranges,and the existence of the time-reversal symmetry of the system results in the symmetrically distributed of Fermi arc surface state with regard to the origin of the coordinate.Next,the influence of nonlocal effects on the Weyl points in gyromagnetic metamaterials with broken time-reversal symmetry and chiral metamaterials with broken spatial inversion symmetry is investigated.Ideal type-I Weyl points can be realized in gyromagnetic metamaterials when the spatial nonlocal effects are considered.The type-I Weyl points,type-II Weyl points,or triply degenerate points can exist in the chiral metamaterials.It can be clearly known from the topological phase diagram that when the nonlocal parameters satisfy a certain range,the type-II Weyl points and the triply degenerate points can exist in a material system at the same time.Furthermore,it is demonstrated that the nontrivial Fermi arc surface state with field-localized properties can be formed on the boundary between the chiral metamaterials and vacuum,which is beneficial for the development of photonic integrated devices.Lastly,the transport properties of copropagating Fermi arc surface states at the interface of gyromagnetic metamaterials with broken time-reversal symmetry and chiral metamaterials with broken spatial inversion symmetry are investigated.Due to the effects of the applied magnetic field and chiral coupling,the gyromagnetic and chiral metamaterials have spatial inversion symmetry and time-reversal symmetry,respectively.According to the bulk-edge correspondence principle,two Fermi arc surface states with the same propagation direction can be supported at the interface of gyromagnetic and chiral metamaterials.Based on the copropagating Fermi arc surface states,two different types of multiplexing optical devices can be constructed:the splitting and merging of surface waves can be achieved in H-junction cross waveguides.Multichannel topological transport of disordered-immune Fermi arc surface states can be controlled by using a T-junction interface configuration.Numerical calculations show that losses affect the band structure of gyromagnetic and chiral metamaterials,but two copropagating Fermi arc surface states still exist at the interface between the gyromagnetic and chiral metamaterials.