Skip to main content
Log in

Splitting rules of electronic miniband in Fibonacci superlattices: a gap map approach

  • Solid State and Materials
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

The splitting rules of fragmental miniband in Fibonacci superlattices (FSLs) with arbitrary basis and generation orders are presented through a gap map diagram. Based on the gap map, we find the invariant conditions of the band structure splitting in the FSL for arbitrary generation orders. Moreover, the band structure splitting can be divided to form many regions, each having a similar pattern. In each region, the widths of most gap bands except two major gaps will decrease for increasing the generation order. It is interesting that the center and gap width of the major gaps will converge to constant values for increasing the generation order of the FSL. Based on the splitting rules displayed in the gap map, it is convenient to predict the fragmental band structure in the FSL for arbitrary generation orders and bases.

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.

Institutional subscriptions

Similar content being viewed by others

References

  • D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53, 1951 (1984)

    Google Scholar 

  • R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, P.K. Battacharya, Phys. Rev. Lett. 55, 1768 (1985)

    Google Scholar 

  • Q. Niu, F. Nori, Phys. Rev. B 42, 10329 (1990)

    Google Scholar 

  • Y. Liu, W. Strakool, Phys. Rev. B 43, 1110 (1991)

    Google Scholar 

  • N. Fujita, K. Niizeki, Phys. Rev. B 64, 144207 (2001)

    Google Scholar 

  • M. Komoto, L.P. Kadanoff, C. Tang, Phys. Rev. Lett. 50, 1870 (1983)

    Google Scholar 

  • V. Kumar, G. Ananthakrishna, Phys. Rev. Lett. 59, 1476 (1987)

    Google Scholar 

  • X.Q. Huang, C.D. Gong, Phys. Rev. B 58, 739 (1998)

    Google Scholar 

  • E. Macia, F. Dominguez-Adame, Phys. Rev. Lett. 76, 2957 (1996)

    Google Scholar 

  • E.L. Albuquerque, M.G. Cottam, Phys. Rep. 376, 225 (2003)

    Google Scholar 

  • E. Macia, Rep. Prog. Phys. 69, 397 (2006)

    Google Scholar 

  • S. Chattopadhyay, A. Chakrabarti, Phys. Rev. B 65, 184204 (2002)

    Google Scholar 

  • M. Naka, K. Ino, M. Kohmoto, Phys. Rev. B 71, 245120 (2005)

    Google Scholar 

  • D. Jin, G. Jin, Phys. Rev. B 71, 014212 (2005)

    Google Scholar 

  • M. Dinu, D.D. Nolte, M.R. Melloch, Phys. Rev. B 56, 1987 (1997)

  • J.E. Zarate, V.R. Velasco, Phys. Rev. B 65, 045304 (2001)

    Google Scholar 

  • P.W. Anderson, Phys. Rev. 109, 1492 (1958)

    Google Scholar 

  • P. Phillips, H.-L. Wu, Science 252, 1805 (1991)

  • J.C. Flores, J. Phys.: Condens. Matter 1, 8471 (1989)

    Google Scholar 

  • W. Kim, L. Covaci, F. Marsiglio, Phys. Rev. B 73, 195109 (2006)

    Google Scholar 

  • F.A.B.F. de Moura, M. Lyra, Phys. Rev. Lett. 81, 3735 (1998)

    Google Scholar 

  • F.M. Izrailev, A.A. Krokhin, Phys. Rev. Lett. 82, 4062 (1997)

    Google Scholar 

  • M. Hilke, J.C. Flores, Phys. Rev. B 55, 10625 (1997)

    Google Scholar 

  • D. Huang, Phys. Rev. B 70, 205124 (2004)

    Google Scholar 

  • A. Esmailpour, M. Esmaeilzadeh, E. Faizabadi, P. Carpena, M.R.R. Tabar, Phys. Rev. B 74, 024206 (2004)

    Google Scholar 

  • M. Stęślicka, R. Kucharczyk, A. Akjouj, B. Djafari-Rouhani, L. Dobrzynski, S.G. Davison, Surf. Sci. Rep. 47, 93 (2002)

    Google Scholar 

  • W.J. Hsueh, H.C. Chen, Phys. Rev. E 76, 057701 (2007)

    Google Scholar 

  • C.L. Roy, A. Khan, Phys. Rev. B 49, 14979 (1994)

    Google Scholar 

  • P. Panchadhyayee, R. Biswas, A. Khan, P.K. Mahapatra, J. Phys.: Condens. Matter 20, 275243 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to W. J. Hsueh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hsueh, W., Chen, C. & Lai, J. Splitting rules of electronic miniband in Fibonacci superlattices: a gap map approach. Eur. Phys. J. B 73, 503–508 (2010). https://doi.org/10.1140/epjb/e2010-00023-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2010-00023-8

Keywords

Navigation