Enhanced Valley Polarization in a Magnetic-Strained Graphene Under the Modulation of the Applied Bias
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ORIGINAL PAPER
Enhanced Valley Polarization in a Magnetic-Strained Graphene Under the Modulation of the Applied Bias Jian-Duo Lu1 Received: 24 March 2020 / Accepted: 15 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract As the potential-wide applications in valleytronic devices, the valleytronics, especially the valley polarization in graphene, has attracted much attentions. Thus, in the present work, we study the effect of the applied bias on the valley polarization in a magnetic-strained graphene, which has been not studied as we know. Concretely, we analyze the dependence of the valley polarization on the magnitude, the position, and the width of the applied bias, and obtain the large valley polarization in such a graphene nanostructure which can be easily controlled by the applied bias. This study can promote the realization of the applied bias-tunable valleytronic devices. Keywords Graphene · Applied bias · Dirac equation · Valley polarization · Continuity of wave functions
1 Introduction In recent years, graphene, especially the valley-dependent transport property of electrons in graphene, has attracted lots of interests [1–6] due to its wide-potential applications in valleytronic devices [7–10] such as valley filters, information processing devices, and information storage devices. However, due to the fact that the key point of realizing the valleytronic devices is to obtain the large valley polarization and find the effective method to control it [11– 14], many researchers have proposed several methods such as applying magnetic fields and/or the strain on a graphene nanostructure [15–18], where the large valley polarization can be easily achieved and controlled through adjusting the magnetic fields and/or the strain. Besides that, in a magnetic-strained graphene, Lu [19] found the large valley polarization which can be easily modulated by the Schottky metal stripe. Zhao et al. [20] observed the significant valley polarization in Co-doped WTe2 via consideration of the spin-orbit coupling, and the polarization can be effectively controlled by the strain force. Especially, Li et al. [21] and Thompson and coworkers [22] obtained the large valley Jian-Duo Lu
l [email protected] 1
Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan, 430081, China
polarization which could be modulated by the external electric field and the external magnetic field B, respectively. Very recently, more and more researchers start to focus on the valley polarization of electrons [23–32] in graphene in order to achieve the large valley polarization, especially the full valley polarization [33, 34] which is very important and pivotal in designing the valleytronic devices. It is worthy to note that, Zhang et al. [35] certainly obtained the full valley polarization in a graphene due to the joint effect of the proton interaction and the pseudomagnetic field. Meanwhile, the perfect valley filtering also has been realized by C
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