Advertisement

Journal of Superconductivity and Novel Magnetism

, Volume 31, Issue 8, pp 2579–2588 | Cite as

First-Principles Calculations of van der Waals and Spin Orbit Effects on the Two-Dimensional Topological Insulator Stanene and Stanene on Ge(111) Substrate

  • M. El Bachra
  • H. Zaari
  • A. Benyoussef
  • A. El Kenz
  • A. G. El Hachimi
Original Paper
  • 145 Downloads

Abstract

The structural and electronic properties of the monolayer and bilayer stanene structures have been studied using first-principles calculations. For the monolayer, the buckled structure is more stable than the flat one, with an opening of the band gap when spin-orbit coupling is taken into account, as mentioned in recent studies. For the bilayer, three types of stacking are considered: parallel layers, anti-parallel layers, and parallel layers where the first layer is shifted from the second one. These three configurations are named AA1, AA2, and AB, respectively. The two layers are separated by the distance d. The interactions between two layers of stanene are strong for a short distance, while the van der Waals bonding appears for a longer distance. Furthermore, stanene was fabricated experimentally on a substrate; thus, we proposed another study of electronic properties of stanene deposited on Ge(111) to reveal other behavior as a topological insulator and show the existence of the quantum spin Hall effect.

Keywords

Topological insulator Electronic and band structure Stanene Ge VdW interaction Spin orbit coupling Band gap 2D materials Quantum Hall effect 

References

  1. 1.
    Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I., Firsov, A.A.: Science 306, 666 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    Vogt, P., De Padova, P., Quaresima, C., Avila, J., Frantzeskakis, E., Asensio, M.C., Resta, A., Ealet, B., Le Lay, G.: Phys. Rev. Lett. 108, 155501 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    Dávila, M., Xian, L., Cahangirov, S., Rubio, A., Le Lay, G.: New J. Phys. 16, 095002 (2014)CrossRefGoogle Scholar
  4. 4.
    Xu, Y., Yan, B., Zhang, H.-J., Wang, J., Xu, G., Tang, P., Duan, W., Zhang, S.-C.: Phys. Rev. Lett. 111, 136804 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    Houmad, M., Zaari, H., Benyoussef, A., El Kenz, A., Ez-Zahraouy, H.: Carbon 94, 1021–1027 (2015)CrossRefGoogle Scholar
  6. 6.
    Ould Ne, M.L., Abbassi, A., El Hachimi, A.G., Benyoussef, A., Ez-Zahraouy, H., El Kenz, A.: Opt. Quant. Electron. 49(6), 218 (2017)CrossRefGoogle Scholar
  7. 7.
    Xu, Y., Yan, B., Zhang, H.-J., Wang, J., Xu, G., Tang, P., Duan, W., Zhang, S.-C.: Phys. Rev. Lett. 111, 136804 (2013)ADSCrossRefGoogle Scholar
  8. 8.
    Modarresi, M., Kakoee, A., Mogulkoc, Y., Roknabadi, M.: Comput. Mater. Sci. 101, 164 (2015)CrossRefGoogle Scholar
  9. 9.
    Rachel, S., Ezawa, M.: Phys. Rev. B 89, 195303 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    van den Broek, B., Houssa, M., Scalise, E., Pourtois, G., Afanasev, V., Stesmans, A.: 2D Materials 1, 021004 (2014)CrossRefGoogle Scholar
  11. 11.
    Wang, G., Zhang, M., Zhu, Y., Ding, G., Jiang, D., Guo, Q., Liu, S., Xie, X., Chu, P.K., Di, Z., Wang, X.: Direct growth of graphene film on germanium substrate. Sci. Rep. vol. 3 (2013)Google Scholar
  12. 12.
    Zhu, F., Chen, W.-J., Xu, Y., Gao, C.-L., Guan, D.-D., Canhua, L., Qian, D., Zhang, S.-C., Jia, J.-F.: arXiv:1506.01601 (accepted by Nature Mater.)
  13. 13.
    Modarresi, M., Kakoee, A., Mogulkoc, Y., Roknabadi, M.R.: Comput. Mater. Sci. 101, 164–167 (2015)CrossRefGoogle Scholar
  14. 14.
    Chuang, F.-C., et al.: Tunable topological electronic structures in Sb(111) bilayers: a first-principles study. Appl. Phys. Lett. 102, 022424 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    Xu, Y., Tang, P., Zhang, S.C.: Phys. Rev. B 92(8), 081112 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I.: J. Phys.: Condens. Matter 21, 395502 (2009)Google Scholar
  17. 17.
    Perdew, J.P., Burke, K., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996)ADSCrossRefGoogle Scholar
  18. 18.
    Perdew, J.P., Zunger, A.: Self-interaction correction to density-functional approximations for many-electron system. Phys. Rev. B 23, 5048 (1981)ADSCrossRefGoogle Scholar
  19. 19.
    Dion, M., Rydberg, H., Schroder, E., Langreth, D.C., Lundqvist, B.I.: Van der Waals density functional for general geometries. Phys. Rev. Lett. 92, 246401 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    Lee, K., Murray, E.D., Kong, L., Lundqvist, B.I., Langreth, D.C.: Higher-accuracy van der waals density functional. Phys. Rev. B 82, 081101(R) (2010)ADSCrossRefGoogle Scholar
  21. 21.
    Perdew, P., Wang, Y.: Accurate and simple density functional for the electronic exchange energy: generalized gradient approximation. Phys. Rev. B 33, 8800 (1986)ADSCrossRefGoogle Scholar
  22. 22.
    Monkhorst, H.J., Pack, J.D.: Phys. Rev. B 13, 5188 (1976)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Tsai, W.-F., Huang, C.-Y., Chang, T.-R., Lin, H., Jeng, H.-T., Bansil, A.: Nat. Commun. 4, 1500 (2013)CrossRefGoogle Scholar
  24. 24.
    Modarresi, M., Kakoee, A., Mogulkoc, Y., Roknabadi, M.R.: Comput. Mater. Sci. 101, 164–167 (2015)CrossRefGoogle Scholar
  25. 25.
    Zhang, R.-W., Zhang, C.-W., Ji, W.-X., Li, S.-S., Yan, S.-S., Hu, S.-J., Li, P., Wang, P.-J., Li, F.: Sci. Rep. 6, 18879 (2016)ADSCrossRefGoogle Scholar
  26. 26.
    Madsen, G.K.H., Singh, D.J.: Comput. Phys. Commun. 175, 67 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    Baroni, S., de Gironcoli, S., Dal Corso, A., Giannozzi, P.: Rev. Mod. Phys. 73, 515–562 (2001)ADSCrossRefGoogle Scholar
  28. 28.
    Liu, C.-C., Feng, W. X., Yao, Y.G.: Quantum spin hall effect in silicene and two-dimensional germanium. Phys. Rev. Lett. 107, 076802 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • M. El Bachra
    • 1
  • H. Zaari
    • 1
  • A. Benyoussef
    • 2
  • A. El Kenz
    • 1
  • A. G. El Hachimi
    • 1
  1. 1.Laboratory of Condensed Matter and Interdisciplinary Sciences (LaMCScI), associé au CNRST (URAC 12), Département de Physique, Faculté des SciencesUniversité Mohammed VRabatMorocco
  2. 2.Hassan II Academy of Science and TechnologyRabatMorocco

Personalised recommendations