Valence Transition And Topological Transition In Topological Kondo Insulator

Topological Kondo insulators such as SmB6 and YbB6 are recently predicted to be a novel class of topological insulator.Unlike general energy band topological insulators,topological Kondo insulators are a strongly correlated system,which topological characteristics are caused by electronic correlations,so it is an ideal system to investigated the effect of electronic correlations on topological systems.At present,using various theoretical tools to get a preliminary understanding of its topology.Sm B6 is a mixed valence system,and the valence state v of Sm^v+ions between 2 and 3.In the past two years,experiments have found that SmB6 undergoes a magnetic transition under pressure,and the valence state v of Sm ions will change drastically near its magnetic transition,increasing from a mixed valence to nearly three valences,called a valence transition.This provides a good theoretical-experimental comparison platform for studying the influence of electronic correlation on topological properties and valence transitions in topological Kondo insulator,and can enhance the understanding of the rich phase transition process in related topological insulator.In this paper,we will conduct a theoretical study on the valence transition of topological Kondo insulators and the related magnetic and topological transitions.In the first chapter,we will first introduce the important theoretical method to be used in this work-the tight bound approximation.Using its quadratic representation,combined with the diagonalization method,we can easily solve the energy band dispersion relationship.The theoretical model and the calculation method of the boson,which will be applied in subsequent chapters.The second chapter will introduce the theoretical model of topological Kondo insulator-Anderson lattice model with spin-orbit coupling,and solve its energy band dispersion,topological characteristics and surface state using the member boson method.The third chapter will introduce additional Coulomb repulsion between d-f electrons on the basis of Anderson lattice model,so as to establish a theoretical model of valence transition,and use the theoretical method of chapter two to solve the valence state when the model parameters change During the evolution process,the valence transition and phase diagram of the paramagnetic phase are obtained.Chapter 4 will calculate the antiferromagnetic transition and the evolution process of the valence state near the antiferromagnetic transition point,and obtain the phase diagram including the antiferromagnetic transition and the valence transition.Chapter 5 will summarize and discuss the main results of this article.The main research findings in this paper are as follows:?1?When the Coulomb correlation strength Udf of the d-f electron exceeds a critical value,as the energy level of the f electron increases,the paramagnetic state will occur from the near-saturated Kondo to the first-order valence transition?FOVT?of the lower mixed valence state,and depending on the parameter conditions,this paramagnetic valence transition can be very close to or converge with the topological transition.?2?Near the paramagnetic valence transition,increasing the temperature will cause a thermodynamic valence transition from the mixed valence to Kondo region,which is also a first-order transition.?3?When Udf is weak,as the energy level of f electron rises,antiferromagnetic transition will occur,which is a second-order transition.But when Udf increases,the antiferromagnetic transition will change from the secondary transition to the first-order transition,along with the valence transition.The research results in this paper can qualitatively explain the valence transition process of SmB6 under pressure,and the correlation among the three phase changes of magnetic transition,topological transition and valence transition can enhance the understanding of rich phase change process in the associated topological insulator.