Theoretical Studies On Topological Properties And Butterfly Spectrum Of Magnons In Photoinduced Two-dimensional Checkerboard Ferromagnets

In recent years,there has been great interest in the topological properties of the spin excitation in insulating quantum magnets.Unlike electrons,magnons are uncharged Bose quasi-particles that are not subject to the Lorentz force and have no conductive and valence bands,which means that the topological magnonic system is a potential candidate for designing devices with low loss and good coherent transport properties.Recently,the topological properties of magnons in the periodically driven two-dimensional insulated ferromagnet have received the attention from more and more researchers.Based on this fact,the topological properties and butterfly spectrum of magnons in the photoinduced two-dimensional insulated ferromagnet with checkerboard lattice structure shall be theoretically studied in this thesis.In chapter 1,the topological phase transition and the Hofstadter butterfly spectrum and the Hofstadter butterfly spectrum in both light-induced electronic and magnon systems are summarized,respectively.In chapter 2,the spin Hamiltonian,spin-wave theory,the Aharonov-Casher effect,and the Floquet-Bloch theory are briefly introduced.In chapter 3,Floquet topological magnon on an irradiated two-dimensional checkerboard ferromagnet and corresponding topological phase transitions are studied.Our results show that the checkerboard Floquet topological magnon insulator can be transformed from a topological magnon insulator into another one possessing various Berry curvatures and Chern numbers by varying the light intensity.Particularly,it is also shown that both Tamm and topologically protected Floquet magnon edge states can appear when a nontrivial gap unfolds.In addition,we display that the sign of the Floquet thermal Hall conductivity is also tunable by changing the strength of the laser field.In Chapter 4,the topological properties of the fractal structure of the Floquet Hofstadter butterfly spectrum of an irradiated two-dimensional insulated ferromagnet with a checkerboard lattice structure are theoretically studied.Firstly,we take into accunt the effects of only space-dependent electric field.Our results display that the magnetic floquet Hofstadt butterfly spectrum has the reflection symmetry.Secondly,the effects of both space-and time-dependent electric field are considered.We find that the fractal structure of the magnetic floquet Hofstadt butterfly spectrum can be tuned by changing laser intensity.What is more,we show the rich topological phase transition associated with different gap openings and band inversion in the magnonic Floquet Hofstadter spectrum.The last chapter is devoted to summarizing and prospecting the present thesis.