High-order Harmonic Generation In Doped Solid With Topological Edge State

When a strong field interacts with matter,many nonlinear responses can take place,one of them is the high-order harmonic generation(HHG).Over the past few decades,researchers have mainly focused on the HHG from gas.HHG in gases have not only been applied to the preparation of extreme ultraviolet and soft X-ray light sources,but also provided a powerful tool for the detection of ultrafast dynamics of attosecond resolution.With the development of laser technology,especially the generation of mid-infrared lasers,the study of HHG has been extended from atoms and molecules to solids.Forming a cross-discipline between strong field physics and solid physics as well as materials science.As targets,solids have higher density and periodic structure in comparison with gases,which not only can generate harmonics more efficiently,but also complicate the generation of solid HHG.So,the study of HHG in different systems has also attracted wide attention.Recently,important condensed matter systems have been investigated by using HHG.The topological properties and phase transition processes of materials have been probed as well as controlled by all-optical method by establishing the dependence between HHG and topological quantum systems.Such as the polarization direction,emission time and harmonic yields of harmonics have been used to determine the topological structure of materials.However,other influencing factors,such as inhomogeneous laser fields and impurity doping effects,are often neglected in the process of using harmonic yields to detect topological phase transitions.As a consequence,this affects the accuracy of distinguishing topological structures and limits the development of optical detection techniques.Based on the above problems,we theoretically investigated the properties of the trivial insulator phase A and the topological insulator phase B transition from metallic case because of the Peierls transition.And then,we investigated the effect of impurity doping on the semiconductor.Then,we found that both the harmonic yields can be significantly enhanced in donor-doped insulator and topological insulator with Phase B compared with the undoped insulator and the trivial insulator with Phase A,respectively.So,we further analyzed the physical mechanism of the two phenomena differing from each other.In addition,we further investigate the HHG of donor-doped trivial and topological insulators.The the main content of this thesis are as follows:Firstly,we investigated the process about the Peierls transition.And we found that the topological insulator Phase B generates isolated topological edge states in the band gap.And the harmonic yields of topological insulator Phase B is significantly enhanced compared to trivial insulator Phase A.This provides a possible observation for the study of topological phase transition of materials.However,the enhanced effect of harmonic yields has been also indicated in the doped impurity material.Then we investigated in effect of doping.And we found that,unlike acceptor-doped material,donor-doped material can enhance the overall harmonic yield because of the localized and isolated states in the band gap.After this,we investigated the mechanism of the influence of topological edge states and donor doped states on harmonic yields.And we found that donor doped states have a main contribution in the harmonic spectrum,unlike the topological edge states.Then we introduce donor-doped impurities in topological materials,and investigate the doping effect on the HHG of topological materials.And the donor doped impurity will enhance the harmonic yield of trivial insulator Phase A,while topological insulator Phase B does not change significantly.This means that we must consider the effect of doping when determining the topological phases by using the difference of harmonic yields.And the robustness of the topological insulator Phase B is also a good way to determine the topological phase.Finally,we investigated the half-occupied impurity KS orbital.And we found that the harmonic yield of Phase A with half-occupied impurity state is higher than that with full-occupied impurity state.In this thesis,we gave a potential method for judging the topological structure of the material.While in the process of studying them,we explain why topological edge states and donor doped states have different effects on harmonics.Our work established a clearer physical picture and providing new ideas as well as theoretical support for the future study of topological phase transitions in experiments.