Research On Dirac Point In Graphene-like Magnonic Crystals

The discovery of quantum Hall effect not only introduced the concept of "condensed state" into the field of mathematical physics,but also attracted great interest of researchers.Condensed matter topological phenomena were first discovered in electronic systems.In recent years,with the birth and development of topological energy band theory,through analogy with electrons,the research of topological phenomena in Artificial Microstructure composites such as photonic crystals and phononic crystals has also made a breakthrough.The properties of boundary state transport predicted by the theory,such as complete backscattering suppression,lossless and unidirectional transmission,have also been confirmed by experiments,this makes it have great application potential.Magnonic crystals is the equivalent of photonic crystals and phononic crystals in the field of magnetism.It is an artificial composite material with periodic structure in the field of magnetism.Due to the Bragg scattering of periodic structure,the propagation of spin wave in the band gap will be restrained.At present,there are relatively few reports on topological phenomena in artificial magnonic crystals.Inspired by many novel physical properties of graphene materials,this paper compares graphene structure with artificial magnonic crystals,extends the study of Dirac point in graphene to two-dimensional honeycomb magnonic crystals with the same symmetry as graphene,and plans to study the Dirac point of artificial magnonic crystals.The topological concept is introduced into the magnon system.Because the topological boundary state spin wave guide has strong robustness,it can be applied to various magnetic devices and application technologies,which greatly improves the stability of the device and has great application prospects in the fields of spin wave guide devices and so on.The innovation of this paper is to combine the graphene material structure with the artificial magnonic crystal system,realize the Dirac point and Dirac-like point in the artificial magnonic crystal system,and regulate the band gap opening width at the Dirac point,which promotes the development of topological magnetic physics.Based on the previous research,this paper uses the knowledge of solid-state physics to carry out theoretical simulation,analysis and calculation.Starting from the graphene-like magnonic crystals,this paper puts forward the hexagonal crystal structure model,deduces the expression of its structure factor,numerically calculates the band structure in the selected region by the optimized plane wave expansion method,and draws the band structure diagram of graphene-like lattice by computer programming,The variation of band gap width with volume filling rate is studied.Secondly,the Dirac point and Dirac-like point are realized by calculating the band structure of the crystal,the Dirac cone and Dirac-like cone are described by their three-dimensional dispersion relationship,and the specific implementation process is systematically explored;The energy field distribution in real space is calculated.Finally,we adjust the structure of the magnonic crystals and change the spatial reflection symmetry of the crystal lattice by changing the ratio of the column in the original cell.Then we control the band gap at the Dirac point and open the inevitable degeneracy caused by the highly symmetrical structure of the lattice,thus forming the valley state of the magnon.It is hoped that through the study of topological physical properties such as Dirac point of artificial magnonic crystals,the regulation and optimization of spin wave can be realized,which provides a feasible scheme for the theoretical design of engineering materials with topological magnonic crystals band gap structure and the production,manufacture and application in real life.