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27/04/2026
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Vo, T. A. T., Dao, T. T., Nguyen, T. T., & Huynh, V. P. (2026). Electronic properties of silicene under non-uniform magnetic field. Dong Thap University Journal of Science, 15(5), 1-10. https://doi.org/10.52714/dthu.ns.2281.1828
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Electronic properties of silicene under non-uniform magnetic field
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Abstract
In this study, we investigate the electronic states according to the single-particle model of silicene under an exponentially decaying magnetic field. By solving the Dirac-Weyl equations, we derive exact expressions for the wave functions and the corresponding Landau level spectrum. We also examine in detail the effects of the electric field, the Zeeman effect, and the non-uniform magnetic field on the probability density and current distributions. Furthermore, we compare our results with those of graphene in the presence of a non-uniform magnetic field.
Keywords
Dirac-Weyl equations, exponentially decaying magnetic field, Silicene
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
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Ghosh, T. K. (2009). Exact solutions for a Dirac electron in an exponentially decaying magnetic field. Journal of Physics: Condensed Matter, 21(4), 045505. https://doi.org/10.1088/0953-8984/21/4/045505
Hoa, L. T., Phuong, L. T. T., Kubakaddi, S. S., Hieu, N. N., & Phuc, H. V. (2022). Landau levels and magneto-optical responses in Weyl semimetal quantum wells in a non-uniform magnetic field. Physical Review B, 106(7), 075412. https://doi.org/10.1103/PhysRevB.106.075412
Kharadi, M. A., Malik, G. F. A., Khanday, F. A., Shah, K. A., Mittal, S., & Kaushik, B. K. (2020). Review—Silicene: From Material to Device Applications. ECS Journal of Solid State Science and Technology, 9(11), 115031. https://doi.org/10.1149/2162-8777/abd09a
Le, T. H., Tran, N. B., Nguyen, N. H., Le, T. N. T., & Huynh, V. P. (2022). Dirac electron in gapped graphene under exponentially decaying magnetic field. Tạp chí Khoa học Đại học Đồng Tháp, 11(5), 35-40. https://doi.org/10.52714/dthu.11.5.2022.978
Liu, C.-C., Jiang, H., & Yao, Y. (2011). Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin. Physical Review B, 84(19), 195430. https://doi.org/10.1103/PhysRevB.84.195430
Muoi, D., Hieu, N. N., Nguyen, C. V., Hoi, B. D., Nguyen, H. V., Hien, N. D., Poklonski, N. A., Kubakaddi, S. S., & Phuc, H. V. (2020). Magneto-optical absorption in silicene and germanene induced by electric and Zeeman fields. Physical Review B, 101(20), 205408. https://doi.org/10.1103/PhysRevB.101.205408
Oughaddou, H., Enriquez, H., Tchalala, M. R., Yildirim, H., Mayne, A. J., Bendounan, A., Dujardin, G., Ait Ali, M., & Kara, A. (2015). Silicene, a promising new 2D material. Progress in Surface Science, 90(1), 46-83. https://doi.org/10.1016/j.progsurf.2014.12.003
Phuc, H. V. (2015). Nonlinear optical absorption via two-photon process in GaAs/Ga1−xAlxAs quantum well. Journal of Physics and Chemistry of Solids, 82, 36-41. https://doi.org/10.1016/j.jpcs.2015.03.004
Phuc, H. V., Hieu, N. N., Dinh, L., & Phong, T. C. (2015). Nonlinear optical absorption in parabolic quantum well via two-photon absorption process. Optics Communications, 335, 37-41. https://doi.org/10.1016/j.optcom.2014.09.004
Roman, R. E., & Cranford, S. W. (2014). Mechanical properties of silicene. Computational Materials Science, 82, 50-55. https://doi.org/https://doi.org/10.1016/j.commatsci.2013.09.030
Shakouri, K., Vasilopoulos, P., Vargiamidis, V., & Peeters, F. M. (2014). Spin- and valley-dependent magnetotransport in periodically modulated silicene. Physical Review B, 90(12), 125444. https://doi.org/10.1103/PhysRevB.90.125444
Wang, D., & Jin, G. (2013). Effect of a nonuniform magnetic field on the Landau states in a biased AA-stacked graphene bilayer. Physics Letters A, 377(40), 2901-2904. https://doi.org/10.1016/j.physleta.2013.08.041
Ezawa, M. (2012). Spin-valley optical selection rule and strong circular dichroism in silicene. Physical Review B, 86(16), 161407. https://doi.org/10.1103/PhysRevB.86.161407
Ghosh, T. K. (2009). Exact solutions for a Dirac electron in an exponentially decaying magnetic field. Journal of Physics: Condensed Matter, 21(4), 045505. https://doi.org/10.1088/0953-8984/21/4/045505
Hoa, L. T., Phuong, L. T. T., Kubakaddi, S. S., Hieu, N. N., & Phuc, H. V. (2022). Landau levels and magneto-optical responses in Weyl semimetal quantum wells in a non-uniform magnetic field. Physical Review B, 106(7), 075412. https://doi.org/10.1103/PhysRevB.106.075412
Kharadi, M. A., Malik, G. F. A., Khanday, F. A., Shah, K. A., Mittal, S., & Kaushik, B. K. (2020). Review—Silicene: From Material to Device Applications. ECS Journal of Solid State Science and Technology, 9(11), 115031. https://doi.org/10.1149/2162-8777/abd09a
Le, T. H., Tran, N. B., Nguyen, N. H., Le, T. N. T., & Huynh, V. P. (2022). Dirac electron in gapped graphene under exponentially decaying magnetic field. Tạp chí Khoa học Đại học Đồng Tháp, 11(5), 35-40. https://doi.org/10.52714/dthu.11.5.2022.978
Liu, C.-C., Jiang, H., & Yao, Y. (2011). Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin. Physical Review B, 84(19), 195430. https://doi.org/10.1103/PhysRevB.84.195430
Muoi, D., Hieu, N. N., Nguyen, C. V., Hoi, B. D., Nguyen, H. V., Hien, N. D., Poklonski, N. A., Kubakaddi, S. S., & Phuc, H. V. (2020). Magneto-optical absorption in silicene and germanene induced by electric and Zeeman fields. Physical Review B, 101(20), 205408. https://doi.org/10.1103/PhysRevB.101.205408
Oughaddou, H., Enriquez, H., Tchalala, M. R., Yildirim, H., Mayne, A. J., Bendounan, A., Dujardin, G., Ait Ali, M., & Kara, A. (2015). Silicene, a promising new 2D material. Progress in Surface Science, 90(1), 46-83. https://doi.org/10.1016/j.progsurf.2014.12.003
Phuc, H. V. (2015). Nonlinear optical absorption via two-photon process in GaAs/Ga1−xAlxAs quantum well. Journal of Physics and Chemistry of Solids, 82, 36-41. https://doi.org/10.1016/j.jpcs.2015.03.004
Phuc, H. V., Hieu, N. N., Dinh, L., & Phong, T. C. (2015). Nonlinear optical absorption in parabolic quantum well via two-photon absorption process. Optics Communications, 335, 37-41. https://doi.org/10.1016/j.optcom.2014.09.004
Roman, R. E., & Cranford, S. W. (2014). Mechanical properties of silicene. Computational Materials Science, 82, 50-55. https://doi.org/https://doi.org/10.1016/j.commatsci.2013.09.030
Shakouri, K., Vasilopoulos, P., Vargiamidis, V., & Peeters, F. M. (2014). Spin- and valley-dependent magnetotransport in periodically modulated silicene. Physical Review B, 90(12), 125444. https://doi.org/10.1103/PhysRevB.90.125444
Wang, D., & Jin, G. (2013). Effect of a nonuniform magnetic field on the Landau states in a biased AA-stacked graphene bilayer. Physics Letters A, 377(40), 2901-2904. https://doi.org/10.1016/j.physleta.2013.08.041
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