Low Energy Topological Excitations In Twodimensional Magnetic Systems

In condensed matter physics,topological band theory for particles and quasiparticles have become an important research field in the past years.In fact,during the study of solid state physics in the last century,it was thought that energy spectrum of materials can show us all information for a long time,which means that only energy eigenvalues are enough.However,even except for topological phase in strong interacting electronic system,there are still many significant phenomena in single particle picture with weak interaction,such as topological insulator,topological semimetal,etc.Therefore,single particle topological phase is an important topic which needs further research.On the other hand,topological band theory also shows the significance of eigenvectors,or eigenwave functions in quantum systems.In the development of topological band theory,there are also many researches among topological quasi-particles such as topological magnons and phonons other than electronic systems.At the same time,scientists have tried to analyze and classify all kinds of topological band materials,which are usually divided into fermionic,bosonic,and anyonic Dirac materials.Due to different commutation relations,there are very different many body properties among different kinds of Dirac materials.Based on magnetic interactions and analysis of topological band structure in single particle picture,this thesis mainly introduces the investigations of spin excitations in various magnetic models with different types of novel lattices and the explorations of possible topological magnonic states.This thesis includes:1.General magnetic interactions are represented and classified by using matrix method.By similar and linear transformation coordinate and rotation transformation are realized for interaction and other manipulations.In addition,it can also be represented and computed in quasi-particle picture.Therefore,real space or momentum space Hamiltonian can be easily obtained.2.Magnetic models in different kinds of lattices are computed,such as hexagonal lattice,Kagome lattice,Lieb lattice,and twisted bilayer hexagonal lattice,etc.Their energy spectrums by analytical or numerical methods are shown,especially the contribution from Dzyaloshinskii–Moriya interaction and pseudo-dipole interaction.3.Based on matrix representation of magnonic Hamiltonian,topological properties of systems are obtained by computing Berry curvature and Chern number.Moreover,thermal Hall conductivity is also provided to understand their chirality and thermal transport behavior.