Spin and spin-valley filter analysis of inner-edge states in hybrid silicene-like nanoribbons

The band structure and the topological property of the silicene-like nanoribbon (SiNR) can be regulated by external fields. The hybrization of SiNRs regulated by external fields may generate some special spin/valley properties of the inner-edge states. In this paper, we introduce three external fields: staggered electric field, antiferromagnetic exchange field and Haldane light field in SiNR systems. We analyze the hybridizations of the two and three SiNRs with 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 SiNR systems. Especially for the hybrid three-ribbon systems, we consider the case only with the inner-edge states. 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.