Study Of Topological Phase Transition Induced By The Polarized Light In The Two-dimensional Lattices

The topological properties of materials as a new classification standard for material states have recently attracted widespread attention.According to the topological properties of the electronic structure of materials,crystalline materials can be divided into two categories:topological trivial and topological nontrivial.According to the new standard for topology division,insulators can be classified into normal insulators and topological insulators.The surface state of topological insulators is not easily damaged by defects and disorder due to topological protection,which makes them potentially important applications in the fields of spintronics and quantum computing.In the past decade,the theoretical predictions and experimental findings of novel topological states have achieved rapid development and remarkable research results.In recent years,more and more new topological phases are expected to be found,the characteristics of Floquet topology insulator,such as the controllability of external periodic field,the realization of large Chern number topological insulators,have attracted extensive attention.In this thesis,we theoretically studied of topological phase transition induced by the polarized light in the two-dimensional lattices.Based on the numerical calculation method to compute the spin Chern number and the Bott index,the topological properties of clean system and disordered systems are studied respectively.The paper is organized as follows four parts:In Section I,we first introduce topology and topological invariants,quantum spin Hall effect and topological insulators.Then,the theoretical tools which are used in the study the topological properties of the two-dimensional lattice,such as the Floquet theorem,numerical calculation method to compute the spin Chern number and the Bott index are introduced.We also introduce the tight binding theory,and some transition terms involved in Hamiltonian in this paper are explained.In Section II,we use Floquet theory to theoretically investigate the influence of the external circularly polarized light on the topological properties of the Lieb lattice with intrinsic spin-orbit coupling.Firstly,we use numerical calculation method to compute the spin Chern number to study the topological properties of the Lieb lattice.The external circularly polarized light makes topological trivial in topological non-trivial systems,and the enhancement of amplitudes of the next nearest-neighbor hopping makes the range of topological trivial phases expand.Next,the effective Hamiltonian in the high-frequency limit is given,and the variations of the energy gaps at different high-symmetry points with the amplitude of the circularly polarized light are theoretically calculated.It is shown that the results from the theoretical calculating in the high-frequency limit are qualitatively consistent with those by numerical calculations.Finally,based on the computation of the Bott index,the influence of disorder on the topological properties of the Lieb lattice with the external circularly polarized light is investigated.The larger the amplitude of the external circularly polarized light,the lower the disorder intensity required for the topological phase transition.The increase of amplitudes of the next nearest-neighbor hopping is beneficial to the stability of the topological non-trivial phase.In section III,We use the Floquet theory to theoretically investigate the influence of the external circularly polarized light on the topological properties of the Kagome lattice with intrinsic spin-orbit coupling.As before,we use numerical calculation method to compute the spin Chern number to study the topological properties of the Kagome lattice.It is shown that the external circularly polarized light causes a large Chern number in the topological non-trivial system.When the amplitude of the circularly polarized light is small,the increase of amplitude of the next nearest-neighbor hopping will cause the system to have a higher Chern number.Next,the effective Hamiltonian of the Kagome lattice in the high-frequency limit is given.Comparing the numerical results and analytical results of the variations of the energy gaps at different high-symmetry points with the amplitude of the circularly polarized light,it is found that they are qualitatively consistent.Finally,based on the computation of the Bott index,the influence of disorder on the topological properties of the Kagome lattice with the external circularly polarized light is also investigated.The larger the amplitude of the external circularly polarized light,the lower the disorder intensity required for the topological phase transition.The increase of amplitudes of the next nearest-neighbor hopping is not beneficial to the stability of the topological non-trivial phase.Finally,we sort out and summarize the work.