Research On The Topological Properties In Low-dimensional Lattice Systems Driven By A Time-periodic Field

In this paper,we have theoretically studied the topological insulator under the Floquet system.By introducing an additional time-periodic electric field into one-dimensional or two-dimensional lattice systems,we study the Floquet topological properties modified by the external field.Particularly,one-dimensional SSH model and two-dimensional graphene lattice are considered in the thesis.These models have first-order topological phase transition and corresponding edge states.After the time-period field is introduced,the time-reversal symmetry is broken,and thus new topological phases are produced.With the help of Floquet theory,we convert the static Hamiltonian into the time-independent effective Hamiltonian in high-frequency approximation.For a special designed time-periodic field,the chiral symmetry of the system can be maintained,under which there exists the nontrivial topological phase.By numerical simulations,we obtain the energy band structures,edge states and topological invariants of the system.The conditions of parameters and symmetries required for the topological phase transition are discussed.To sum up,we have verified by the Floquet theory that the introduction of the time-periodic field will bring the topological phase transition in the considered system.The condition for the nontrivial Floquet topological phase is given analytically.The topological state is confirmed by the analysis of symmetry,discussion of topological classification and calculation of topological invariant.In terms of physical realization,this model can be easily realized in the quantum dot array,in graphene,or in the cold atom system.The results here show that the time-periodic driven system has prospective application in the nano electronic device with strong robustness.