Spin And Spin-valley Filter Analysis Of Inner-edge States In Hybrid Single-layer Topological Insulator Nanoribbons

With the development of science and technology,the performance of microelectronic devices is more and more demanding.Both the spin and the valley information of the electrons can be used as information carriers like electric charges,thus giving birth to spintronics and valleytronics.Microelectronics related to the spintronics and the valleytronics has the advantages of low power consumption,high speed and high integration.So more and more researches have been employed on how to control spin and valley degrees of freedom.This led to the exploration of other monolayer materials.In particular,monolayer topological materials: Silicene,Germanene,and Stanene are called Quantm spin Hall(QSH)insulators,the nanoribbon of which has helical edge state.Because these monolayer materials have controllable spin and valley degrees of freedom at the same time,they have a very broad application prospect in devices with spintronics and valleytronics.Compared with graphene,silicene germanene and stanene have a larger spin-orbit coupling,and their energy gap can be further adjusted by the external field due to their low buckling geometry.The large spin orbit(SO)coupling of silience germanene and stanene leads to the Hall effect and the spin hall effect,which are related to the spin/valley of electrons.By applying the external field(such as electric field,Haldane light field,antiferromagnetic exchange field,etc.),the energy gap can be closed and opened,so that the monolayer topological materials can undergo topological phase transition.Due to the size limitation,there is no topological valley edge state in the nonoribbons of monolayer materials.But the topological valley edge states appeared at the interface between two different topological insulator phases.However,the related valley edge state appears at the interface between two nanoribbons with different topological phases.At present,spin filters and spin valley filters of inner-edge states have outer-edge states,and the existence of antiferromagnetic exchange field and Haldane light field are not considered.In addition,according to the topological characteristics of the hybrid nanoribbons of monolayer,the spin and spin valley filters based on their inner-edge states have not been fully analyzed.Therefore,this paper has studied these deficiencies in depth.Based on the tight-binding model and the Dirac equation,we analyze the relevant theories of the topological phase transitions of silliene,germanene and stanene.The topological phase transitions are usually determined by four independent Dirac mass terms.We then introduce three external fields: staggered electric field,antiferromagnetic exchange field and Haldane light field into monolayer topological insulator system.We analyze the hybridizations of the two and three monolayer topological-insulator nanoribbons in which two adjacent nanoribbons in different topological states,which generate the inner-edge states with some spin and valley properties.These hybrid systems may be used as the spin filter and spin-valley filter.We give the systematical and detailed investigations on these inner-edge-state spin and spin-valley filter properties for these hybrid systems.Especially for the hybrid three-ribbon systems,we consider the case only with the inner-edge states.Based on the above conditions,seven kinds of filters are summarized.Furthermore,we observe that the inner-edge state is robust against the weak Rashba spin-orbit coupling,the moderate disorder and the outer imperfections.In addition,the inner-edge state is absolutely broken as the vacancy is in the inner edge.We believe these inner-edge-state spin/valley filters have very wide applications in the future spintronic and valleytronic devices.