Antiferromagnetic State In Topological Kondo-Lattice Model

Investigation of strongly correlated electron systems play a significant role in the development of condensed matter physics.As an important theoretical model to describe electron correlation in topology states of matter,the topological Kondo lattice model has attracted much interest among condensed matter community.In this thesis,based on the antiferromagnetic spin-wave theory,we use the mean-field approach to study and summarize the phase diagram of Kane-Mele-Kondo lattice model and conduction electron magnetization of Kondo-Heisenberg mod-el.The thesis is divided into five chapters.In chapter one,we introduce the new physics which caused by topology and interaction,especially the discovery of topological antiferromagnetic spin-density-wave on extended Hubbard model inspires us to explore novel topological state of matter.In chapter two,the spin-wave theory is used to deal with Heisenberg model,and we have calculated the solution of spin-wave and dispersion relation for this model on the square and the honeycomb lattice;It is found that the influence of spin fluctuation to magneti-zation is closely related to dimension of the system by calculating magnetization of different lattice structures.In chapter three,we directly use mean-field decou-pling to explore the ground-state energy of the Kane-Mele-Kondo lattice model on the honeycomb lattice,and we find magnetization of conduction electron changes with next-nearest-neighbor hopping t?and Kondo-coupling J_?;particularly,we focus on its magnetic properties,which are important in many realistic heavy-fermion materials.Besides the Kondo insulator,two kinds of antiferromagnetic spin-density-wave phases are discovered.One is the normal antiferromagnetic spin-density-wave state?N-SDW?and the other is a nontrivial topological anti-ferromagnetic spin-density-wave state?T-SDW?,which shows the unexpected Z₂topological order with a quantized spin Hall conductance and a helical edge s-tate.Interestingly,the transition between the two spin-density-wave phases is an exotic topological quantum phase transition,whose critical behavior is described by an emergent three-dimensional quantum electrodynamics.In chapter four,we concentrate our attention to the topological Kondo-Heisenberg model on the hon-eycomb lattice.When system only lies in the rigid fully polarized antiferromag-netic state,we find that magnetization of conduction electron changes with next-nearest-neighbor hopping t^?and Kondo-coupling J_?at zero temperature.When considering the quantum correction from the interaction between spin-wave and magnetic polarization of conduction electron,Hartree-Fock approximate method is used.By solving two self-consistent Hartree-Fock equations,it is found that the total magnetization of conduction electron and spin is changed with tuning mean-field parameters of the system.In the last chapter,we summarize related works on topological Kondo lattice model and suggest some interesting issues for further investigation.