Research On Topological Properties Of Dirac Point And Flat Band In Two-dimensional Magnonicic Crystals With Honeycomb-Kagome Structure

The Quantum Hall effect has pioneered a new direction in the field of Condensed matter physics,and also introduced the concept of "topology" in mathematics into physics research.The condensed state topological phenomenon was first discovered in electronic systems.In recent years,with the birth and development of topological band theory,the study of topological phenomena in artificial microstructure composite materials such as photonic crystals and phononic crystals has also made breakthrough progress through analogy with electrons.The predicted boundary state transport properties of complete backscattering suppression,lossless and unidirectional transmission have also been experimentally confirmed,This gives it great potential for application.Artificial Magnonic crystals have great similarities with photonic and phononic crystals,and have important research value in the field of ferromagnetism.They have periodic structures,so they are subject to the Bragg scattering of periodic structures,and the propagation of spin waves in the band gap will be suppressed.From the research of relevant literature,their own topological research is relatively small,and they are inspired by many novel physical properties of Graphene materials,In this paper,the model of artificial Magnonic crystal with Graphene like structure is constructed,the concept of artificial Magnonic crystal with Honeycomb Kagome structure is proposed,and the conditions for the generation of Dirac points and topological flat bands and their regulation are numerically studied.The topological concept is introduced into the artificial Magnonic crystal system.Due to the topological stability,the generation of Dirac points,flat bands and other topological states in the Magnonic crystal can be applied to various spin wave magnetic devices and application technologies,which can improve the stability of devices and be more conducive to the production of spin wave related stabilizing devices.The structure of Graphene has good symmetry and periodicity,which makes it show good conductivity,thermal conductivity and Dirac point in different crystal materials.Kagome structure lattice is a two-dimensional network structure composed of common triangles arranged in a hexagon.This unique geometric structure makes its electronic structure including a colorless flat band,Graphene like Dirac cone and Van Hove singularity,etc.,showing many strange characteristics.The innovation of this paper is to link the Graphene structure with the unique structure of Kagome,and combine the Graphene material structure with the artificial Magnonic crystal to study its topological properties.By adjusting the radius ratio of cylindrical scatterers at different grid points,the possibility of generating and regulating Dirac points and topological flat bands in the artificial Magnonic crystal system can be realized.It is obvious that with the development of artificial micro and nano processing manufacturing technology,this control scheme is feasible in practice.Subsequently,through extensive numerical calculations,the paper studied the laws of Dirac point and flat band changes,which expanded the research and application fields of magnetic topology condensed matter physics.In the next part,we also study the numerical calculation feasibility of the related topological parameters in the field of magnetism,such as Chen number and Bailey curvature,and clarify their value in artificial Magnonic crystals;Taking a two-dimensional square lattice Magnonic crystal as an example,Bailey curvature and number of spin waves in momentum space are studied by theoretical derivation and numerical calculation,in order to expand the study of topological physical properties of Magnonic crystals.