Skip to main content
Log in

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

  • Original Paper
  • Published:
Journal of Superconductivity and Novel Magnetism Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  3. Dávila, M., Xian, L., Cahangirov, S., Rubio, A., Le Lay, G.: New J. Phys. 16, 095002 (2014)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  5. Houmad, M., Zaari, H., Benyoussef, A., El Kenz, A., Ez-Zahraouy, H.: Carbon 94, 1021–1027 (2015)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  8. Modarresi, M., Kakoee, A., Mogulkoc, Y., Roknabadi, M.: Comput. Mater. Sci. 101, 164 (2015)

    Article  Google Scholar 

  9. Rachel, S., Ezawa, M.: Phys. Rev. B 89, 195303 (2014)

    Article  ADS  Google Scholar 

  10. van den Broek, B., Houssa, M., Scalise, E., Pourtois, G., Afanasev, V., Stesmans, A.: 2D Materials 1, 021004 (2014)

    Article  Google Scholar 

  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)

  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. Modarresi, M., Kakoee, A., Mogulkoc, Y., Roknabadi, M.R.: Comput. Mater. Sci. 101, 164–167 (2015)

    Article  Google Scholar 

  14. Chuang, F.-C., et al.: Tunable topological electronic structures in Sb(111) bilayers: a first-principles study. Appl. Phys. Lett. 102, 022424 (2013)

    Article  ADS  Google Scholar 

  15. Xu, Y., Tang, P., Zhang, S.C.: Phys. Rev. B 92(8), 081112 (2015)

    Article  ADS  Google Scholar 

  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. Perdew, J.P., Burke, K., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996)

    Article  ADS  Google Scholar 

  18. Perdew, J.P., Zunger, A.: Self-interaction correction to density-functional approximations for many-electron system. Phys. Rev. B 23, 5048 (1981)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  21. Perdew, P., Wang, Y.: Accurate and simple density functional for the electronic exchange energy: generalized gradient approximation. Phys. Rev. B 33, 8800 (1986)

    Article  ADS  Google Scholar 

  22. Monkhorst, H.J., Pack, J.D.: Phys. Rev. B 13, 5188 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  23. Tsai, W.-F., Huang, C.-Y., Chang, T.-R., Lin, H., Jeng, H.-T., Bansil, A.: Nat. Commun. 4, 1500 (2013)

    Article  Google Scholar 

  24. Modarresi, M., Kakoee, A., Mogulkoc, Y., Roknabadi, M.R.: Comput. Mater. Sci. 101, 164–167 (2015)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  26. Madsen, G.K.H., Singh, D.J.: Comput. Phys. Commun. 175, 67 (2006)

    Article  ADS  Google Scholar 

  27. Baroni, S., de Gironcoli, S., Dal Corso, A., Giannozzi, P.: Rev. Mod. Phys. 73, 515–562 (2001)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. G. El Hachimi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bachra, M.E., Zaari, H., Benyoussef, A. et al. First-Principles Calculations of van der Waals and Spin Orbit Effects on the Two-Dimensional Topological Insulator Stanene and Stanene on Ge(111) Substrate. J Supercond Nov Magn 31, 2579–2588 (2018). https://doi.org/10.1007/s10948-017-4503-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10948-017-4503-9

Keywords

Navigation