Study On The Energy Band And Topological Edge State Properties Of Graphene And Phosphorene Under Light

In the past few decades,the field of condensed matter physics has developed by leaps and bounds.The discovery of two-dimensional materials and the introduction of topology have brought tremendous development to this field.Researchers have discovered many topological materials and topological phenomena in static systems,such as topological insulators,quantum Hall effect,body-edge correspondence,etc.The time driven system has more abundant topological phenomena,and the topological properties can be easily controlled by changing the periodically driving field.In recent years,time driven system has gained more and more attention.The main research method for periodically driven quantum systems is the Floquet theorem.Researchers have found that the periodically driven system can be transformed into a quasi-static system under the framework of Floquet theory.And many properties which are difficult to be obtained or do not exist in static system,could arise in Floquet system.In recent years,experimental observations of Floquet states and verification of Floquet energy bands have further impelled researchers to devote to the Floquet systems.In this paper,we use circularly polarized light as the periodically driving field to study the properties of energy band and topological edge states of graphene and materials as two-dimensional materials.In the first chapter,we briefly introduced the Floquet theorem and related research progress,as well as the concepts of two-dimensional materials and topology.In the second chapter,we introduced the energy band theory of the tight-binding model,Floquet theory topological concepts,and related calculation methods in more depth.In chapter three,we calculated and analyzed the Floquet energy band properties,topological phase transitions,and properties of topological edge states in graphene under a periodically driven light field.Through calculation,we found that,in addition to the ordinary topological phase of ?1 Chern number and the corresponding edge state,there are the topological phase and the photo-induced edge state that corresponding to the high Chern number at low driven frequencies,and there is a physical relationship between these topological edge states and the Chern number of bulk materials.Besides,we also found that the electronic state density distribution of these edge states has a corresponding relationship with the Floquet sub-band index,and we described the size effect of these edge states.In chapter four,we take phosphorene as the research object,calculated and analyzed the properties of the Floquet energy bands and topological edge states of phosphorene under light field,and described its size effect.In the last chapter,we summarized this article and looked forward to future work.