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.
By the Floquet theory, we transform the Su–Schrieffer–Heeger model with the periodically modulated nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions into an effective 2D model, which holds the total Chern number of ±1 modulated by the parameter θ. Under a staggered electric potential, the topological phase diagrams of the effective 2D model are reshaped and similar to the well-known Haldane model. While under a staggered Zeeman field, the topological phase diagram has the same shape as the former case, but with different Chern numbers, such as the spin and valley Chern numbers. With the combination of the staggered Zeeman field and the electric field, the effective 2D model holds even richer topological phases. At last, we find some types of topological pump, which can generate the time-averaged current without any bias voltage. The current depends on their different Chern numbers. In other words, we can modulate the parameters to obtain various Chern numbers to control the topological pump.
We use the spin and valley degrees of freedom to design the bipolar and unipolar valley filter effects based on the graphene-based P/N junction. When the modified Haldane model and staggered potential are applied on the region P, while the off-resonant circularly polarized light and staggered ferromagnetic exchange field are applied on the region N, the unipolar valley filter effect emerges with the unidirectional spin–valley current. The direction and type of the unidirectional spin–valley current depend on the phase of the modified Haldane model and the direction of polarized light. Other types of the bipolar valley filter effects are also reported, such as the valley-mixed bipolar spin filter effect, valley-mixed bipolar filter effect, valley-locked bipolar spin filter effect and valley-locked bipolar filter effect. These bipolar filter effects have the similarity that the spin–valley currents flow bidirectionally. These types of the unipolar and bipolar valley filter effects can be also mutually switched by modulating the external fields. Moreover, these unipolar and bipolar valley filter effects are robust against a weak temperature. This work reveals that the graphene-based junction has the potential applications in designing the valley filter device and improving the reprogrammable spin logic.
In this work, we investigate the topological phase transitions and corresponding transport properties in zigzag stanene nanoribbon with different magnetism. The results show that the off-resonant circularly polarized (ORCP) light may induce anisotropic chiral edge state with a magnetic phase transition from antiferromagnetic state to nonmagnetic state. In combination with the ORCP light and electric field, the 100% spin-polarized edge state can be induced with some magnetic orders. The finite-size effect is also an important factor for the magnetic phase transitions, which in turn induces topological phase transitions from the band insulator to topological phases. By constructing the topological-insulator junctions with some topological edge states, we further study the Fabry-Perot resonant, where multiple reflection edge states cause strong current loops. By modulating the ORCP and electric field, the system can also be regarded as a switcher, to control the charge current or spin polarized current. These findings pave a way for designing topological device with magnetic edges in the future nano spintronics.
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