Skip to main content
SpringerLink
Log in

Density-Functional and Tight-Binding Theory of Silicene and Silicane

  • Chapter
  • First Online:
Silicene

Part of the book series: NanoScience and Technology ((NANO))

  • 814 Accesses

Abstract

A combination of density functional theory and a tight-binding model offers a robust means to describe the structure, vibrations, and electronic states of silicene. In this chapter we give an overview of the electronic structure and phonon dispersions of silicene and its fully hydrogenated derivative, silicane. We discuss the dynamical stability of the buckled silicene and silicane lattices and we present their phonon dispersions. We discuss the first-principles electronic band structure of ideal, free-standing silicene, paying particular attention to the small band gap opened by spin–orbit coupling, which renders the material a topological insulator. We look at the tight-binding description of silicene and examine the effects of an external electric field which, above a critical electric field, counters the spin–orbit gap and triggers a phase transition into a band-insulator state in which the band gap is linearly tunable by the electric field. We also present the tight-binding description of silicane which, parameterised by density functional theory, sheds light on the importance of long-range hopping in this material.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)

    Article  ADS  Google Scholar 

  2. A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)

    Article  ADS  Google Scholar 

  3. S. Cahangirov, M. Topsakal, E. Aktürk, H. Şahin, S. Ciraci, Phys. Rev. Lett. 102, 236804 (2009)

    Article  ADS  Google Scholar 

  4. N.D. Drummond, V. Zólyomi, V.I. Fal’ko, Phys. Rev. B 85, 075423 (2012)

    Article  ADS  Google Scholar 

  5. P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M.C. Asensio, A. Resta, B. Ealet, G. Le Lay, Phys. Rev. Lett. 108, 155501 (2012)

    Article  ADS  Google Scholar 

  6. B. Feng, Z. Ding, S. Meng, Y. Yao, X. He, P. Cheng, L. Chen, K. Wu, Nano Lett. 12, 3507 (2012)

    Article  ADS  Google Scholar 

  7. L. Chen, C.-C. Liu, B. Feng, X. He, P. Cheng, Z. Ding, S. Meng, Y. Yao, K. Wu, Phys. Rev. Lett. 109, 056804 (2012)

    Article  ADS  Google Scholar 

  8. C.L. Lin, R. Arafune, K. Kawahara, M. Kanno, N. Tsukahara, E. Minamitani, Y. Kim, M. Kawai, N. Takagi, Phys. Rev. Lett. 110, 076801 (2013)

    Article  ADS  Google Scholar 

  9. L. Chen, H. Li, B. Feng, Z. Ding, J. Qiu, P. Cheng, K. Wu, S. Meng, Phys. Rev. Lett. 110, 085504 (2013)

    Article  ADS  Google Scholar 

  10. P. De Padova, P. Vogt, A. Resta, J. Avila, I. Razado-Colambo, C. Quaresima, C. Ottaviani, B. Olivieri, T. Bruhn, T. Hirahara, T. Shirai, S. Hasegawa, M.C. Asensio, G. Le Lay, Appl. Phys. Lett. 102, 163106 (2013)

    Article  ADS  Google Scholar 

  11. A. Resta, T. Leoni, C. Barth, A. Ranguis, C. Becker, T. Bruhn, P. Vogt, G. Le Lay, Sci. Rep. 3, 2399 (2013)

    Article  ADS  Google Scholar 

  12. A.J. Mannix, B. Kiraly, B.L. Fisher, M.C. Hersam, N.P. Guisinger, ACS Nano 8, 7538 (2014)

    Article  Google Scholar 

  13. L. Tao, E. Cinquanta, D. Chiappe, C. Grazianetti, M. Fanciulli, M. Dubey, A. Molle, D. Akinwande, Nat. Nanotechnol. 10, 227 (2015)

    Article  ADS  Google Scholar 

  14. P.R. Wallace, Phys. Rev. 71, 622 (1947)

    Article  ADS  Google Scholar 

  15. Z. Ni, Q. Liu, K. Tang, J. Zheng, J. Zhou, R. Qin, Z. Gao, D. Yu, J. Lu, Nano Lett. 12, 113 (2012)

    Article  ADS  Google Scholar 

  16. C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)

    Article  ADS  Google Scholar 

  17. M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)

    Article  ADS  Google Scholar 

  18. X.-L. Qi, S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)

    Article  ADS  Google Scholar 

  19. Y. Kubota, K. Watanabe, O. Tsuda, T. Taniguchi, Science 317, 932 (2007)

    Article  ADS  Google Scholar 

  20. M.P. Levendorf, C.-J. Kim, L. Brown, P.Y. Huang, R.W. Havener, D.A. Muller, J. Park, Nature 488, 627 (2012)

    Article  ADS  Google Scholar 

  21. K.F. Mak, C. Lee, J. Hone, J. Shan, T.F. Heinz, Phys. Rev. Lett. 105, 136805 (2010)

    Article  ADS  Google Scholar 

  22. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti, A. Kis, Nat. Nanotechnol. 6, 147 (2011)

    Article  ADS  Google Scholar 

  23. B. Radisavljevic, M.B. Whitwick, A. Kis, ACS Nano 5, 9934 (2011)

    Article  Google Scholar 

  24. T. Georgiou, R. Jalil, B.D. Belle, L. Britnell, R.V. Gorbachev, S.V. Morozov, Y.-J. Kim, A. Gholinia, S.J. Haigh, O. Makarovsky, L. Eaves, L.A. Ponomarenko, A.K. Geim, K.S. Novoselov, A. Mishchenko, Nat. Nanotechnol. 8, 100 (2013)

    Article  ADS  Google Scholar 

  25. J.N. Coleman, M. Lotya, A. O’Neill, S.D. Bergin, P.J. King, U. Khan, K. Young, A. Gaucher, S. De, R.J. Smith, I.V. Shvets, S.K. Arora, G. Stanton, H.-Y. Kim, K. Lee, G.T. Kim, G.S. Duesberg, T. Hallam, J.J. Boland, J.J. Wang, J.F. Donegan, J.C. Grunlan, G. Moriarty, A. Shmeliov, R.J. Nicholls, J.M. Perkins, E.M. Grieveson, K. Theuwissen, D.W. McComb, P.D. Nellist, V. Nicolosi, Science 331, 568 (2011)

    Article  ADS  Google Scholar 

  26. C. Ataca, H. Sahin, S. Ciraci, J. Phys. Chem. C 116, 8983 (2012)

    Article  Google Scholar 

  27. D. Braga, L.I. Gutiérrez, H. Berger, A.F. Morpurgo, Nano Lett. 12, 5218 (2012)

    Article  ADS  Google Scholar 

  28. A. Kormányos, V. Zólyomi, N.D. Drummond, P. Rakyta, G. Burkard, V.I. Fal’ko, Phys. Rev. B 88, 045416 (2013)

    Article  ADS  Google Scholar 

  29. A. Kormányos, V. Zólyomi, N.D. Drummond, G. Burkard, Phys. Rev. X 4, 011034 (2014)

    Google Scholar 

  30. A. Kormányos, G. Burkard, M. Gmitra, J. Fabian, V. Zólyomi, N.D. Drummond, V. I. Fal’ko, 2D Mater. 2, 022001 (2015)

    Article  Google Scholar 

  31. D. MacNeill, C. Heikes, K.F. Mak, Z. Anderson, A. Kormányos, V. Zólyomi, J. Park, D.C. Ralph, Phys. Rev. Lett. 114, 037401 (2015)

    Google Scholar 

  32. V. Zólyomi, N.D. Drummond, V.I. Fal’ko, Phys. Rev. B 87, 195403 (2013)

    Article  ADS  Google Scholar 

  33. V. Zólyomi, N.D. Drummond, V.I. Fal’ko, Phys. Rev. B 89, 205416 (2014)

    Article  ADS  Google Scholar 

  34. F. Liu, H. Shimotani, H. Shang, T. Kanagasekaran, V. Zólyomi, N. Drummond, V.I. Fal’ko, K. Tanigaki, ACS Nano 8, 752 (2014)

    Article  Google Scholar 

  35. G.W. Mudd, A. Patanè, Z.R. Kudrynskyi, M.W. Fay, O. Makarovsky, L. Eaves, Z.D. Kovalyuk, V. Zólyomi, V. Falko, Appl. Phys. Lett. 105, 221909 (2014)

    Article  ADS  Google Scholar 

  36. D.C. Elias, R.R. Nair, T.M.G. Mohiuddin, S.V. Morozov, P. Blake, M.P. Halsall, A.C. Ferrari, D.W. Boukhvalov, M.I. Katsnelson, A.K. Geim, K.S. Novoselov, Science 323, 610 (2009)

    Article  ADS  Google Scholar 

  37. E. Bianco, S. Butler, S. Jiang, O.D. Restrepo, W. Windl, J.E. Goldberger, ACS Nano 7, 4414 (2013)

    Article  Google Scholar 

  38. V. Zólyomi, J.R. Wallbank, V.I. Fal’ko, 2D Mater. 1, 011005 (2014)

    Article  Google Scholar 

  39. S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.I.J. Probert, K. Refson, M.C. Payne, Z. Kristallogr. 220, 567 (2005)

    Google Scholar 

  40. K. Refson, P.R. Tulip, S.J. Clark, Phys. Rev. B 73, 155114 (2006)

    Article  ADS  Google Scholar 

  41. G. Kresse, J. Furthmüller, Phys. Rev. B 54, 11169 (1996)

    Article  ADS  Google Scholar 

  42. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

    Article  ADS  Google Scholar 

  43. J. Heyd, G.E. Scuseria, M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)

    Article  ADS  Google Scholar 

  44. A.V. Krukau, O.A. Vydrov, A.F. Izmaylov, G.E. Scuseria, J. Chem. Phys. 125, 224106 (2006)

    Article  ADS  Google Scholar 

  45. G.P. Francis, M.C. Payne, J. Phys.: Condens. Matter 2, 4395 (1990)

    ADS  Google Scholar 

  46. R. Winkler, U. Zülicke, Phys. Rev. B 82, 245313 (2010)

    Article  ADS  Google Scholar 

  47. L. Pan, H.J. Liu, Y.W. Wen, X.J. Tan, H.Y. Lv, J. Shi, X.F. Tang, Phys. Lett. A 375, 614 (2011)

    Article  ADS  Google Scholar 

  48. M. Houssa, A. Dimoulas, A. Molle, J. Phys.: Condens. Matter 27, 253002 (2015)

    ADS  Google Scholar 

  49. P.E. Blöchl, Phys. Rev. B 50, 17953 (1994)

    Article  ADS  Google Scholar 

  50. F. Favot, A.D. Corso, Phys. Rev. B 60, 11427 (1999)

    Article  ADS  Google Scholar 

  51. L.C. Lew Yan Voon, E. Sandberg, S. Aga, A.A. Farajian, Appl. Phys. Lett. 97, 163114 (2010)

    Article  ADS  Google Scholar 

  52. M. Houssa, E. Scalise, K. Sankaran, G. Pourtois, V.V. Afanas’ev, A. Stesmans, Appl. Phys. Lett. 98, 223107 (2011)

    Article  ADS  Google Scholar 

  53. J.C. Garcia, D.B. de Lima, L.V.C. Assali, J.F. Justo, J. Phys. Chem. C 115, 13242 (2011)

    Article  Google Scholar 

  54. O. Pulci, P. Gori, M. Marsili, V. Garbuio, R. Del Sole, F. Bechstedt, Eur. Phys. Lett. 98, 37004 (2012)

    Article  ADS  Google Scholar 

  55. W. Wei, T. Jacob, Phys. Rev. B 88, 045203 (2013)

    Article  ADS  Google Scholar 

  56. J.O. Sofo, A.S. Chaudhari, G.D. Barber, Phys. Rev. B 75, 153401 (2007)

    Article  ADS  Google Scholar 

  57. S. Park, B. Lee, S.H. Jeon, S. Han, Curr. Appl. Phys. 11, S337 (2011)

    Article  ADS  Google Scholar 

  58. L. Liu, Z. Shen, Appl. Phys. Lett. 95, 252104 (2009)

    Article  ADS  Google Scholar 

  59. J.C. Slater, G.F. Koster, Phys. Rev. 94, 1498 (1954)

    Article  ADS  Google Scholar 

  60. C.-C. Liu, W. Feng, Y. Yao, Phys. Rev. Lett. 107, 076802 (2011)

    Article  ADS  Google Scholar 

  61. G.W. Semenoff, V. Semenoff, F. Zhou, Phys. Rev. Lett. 101, 087204 (2008)

    Article  ADS  Google Scholar 

  62. H. Hakan Gürel, V. Ongun Özçelik, S. Ciraci, J. Phys. Condens. Matter 25, 305007 (2013)

    Google Scholar 

  63. C.-C. Liu, H. Jiang, Y. Yao, Phys. Rev. B 84, 195430 (2011)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Graphene Institute, University of Manchester, Booth Street East, Manchester, M13 9PL, UK

    V. Zólyomi, J. R. Wallbank & V. I. Fal’ko

  2. Physics Department, Lancaster University, Lancaster, LA1 4YB, UK

    N. D. Drummond

Authors
  1. V. Zólyomi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. D. Drummond
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. R. Wallbank
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. I. Fal’ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Fal’ko .

Editor information

Editors and Affiliations

  1. Institut für Physik, Technische Universität Chemnitz, Chemnitz, Germany

    Patrick Vogt

  2. CNRS, PIIM UMR 7345, Aix-Marseille University, Marseille, France

    Guy Le Lay

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zólyomi, V., Drummond, N.D., Wallbank, J.R., Fal’ko, V.I. (2018). Density-Functional and Tight-Binding Theory of Silicene and Silicane. In: Vogt, P., Le Lay, G. (eds) Silicene. NanoScience and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-99964-7_2

Download citation

Publish with us

Policies and ethics

Search

Navigation