Topological edge states have crucial applications in nano spintronics and valleytronics devices, while topological inner-edge states have seldom been extensively researched in this field. Based on the inner-edge states of the hybridized zigzag silicene-like nanoribbons, we investigate their transport properties. We propose two types of spin-valley filters. The first type can generate two different spin-valley polarized currents in output leads, respectively. The second type outputs the specific spin-valley polarized current in only one of the output leads. All these inner-edge states have the spin-valley-momentum locking property. These types of filters can switch the output spin-valley polarizations by modulating the external fields. Besides, we also find that the device size plays a crucial role in designing these spin-valley filters. Moreover, the local current distributions are calculated to visualize the detailed transport process and understand the mechanism. The mechanism lies that the spin-valley polarized current can nearly freely pass through the system with the same momentum, spin and valley degrees of freedom. The small reflection of the current results from the inter-valley scattering. In particular, we also consider the realistic (disorder) effects on the performance of these filters to ensure the robustness of our systems. We believe these spin-valley current filtering effects have potential applications in the future spintronics and valleytronics device designs.

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Understand the spin and current behavior in the topological-insulator (TI) system is crucial for the design of electronic and spintronic devices. To study these behaviors, some three-terminal hetero-junction TI systems made from the zigzag silicene-like nanoribbons (ZSiNRs) are investigated. Different external fields are applied in the leads and conductor regions, which result in the expected topological edge states. By calculating the local current distribution, we find two important characteristics of topological edge current propagating in these systems. Firstly, the topological edge current prefers to flow into the nearest channel, rather than the other faraway channels. Secondly, the group-velocity mismatch as a scattering engineering has a significant effect on current propagation behavior. In other words, one can manipulate the topological edge current by velocity mismatch. Based on these characteristics, a type of three-terminal spin filter is proposed in this paper. Moreover, some interesting transport phenomena such as space-separated Fano-resonance are also discovered in the TI-junction systems.

We investigate the formation of inner edge states and their transport properties in hybrid nanoribbons. Some new inner edge states, such as spin-polarized, spin-valley-polarized and valley-polarized antichiral inner edge states, are obtained, different from the current existence of valley- and spin-valley-momentum locked inner edge states. We also obtain general formula of local bond current with the wave-function matching technique and use it to discover three interesting transport phenomena of the intravalley and intervalley scatterings that depend on the propagating direction, propagating path, spin mode and wave-vector mismatches between inner edge states. In particular, these transport phenomena are further used to design topological spin, spin-valley and valley filters and be representative for graphene, silicene, germanene and stanene, supporting a potential application of inner edge states, which are robust against random vacancies.

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