The European Physical Journal B

, Volume 73, Issue 4, pp 503–508 | Cite as

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

Solid State and Materials

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.

Keywords

Band Structure Generation Order Bloch Wave Fibonacci Sequence Splitting Rule 

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References

  1. D. Shechtman, I. Blech, D. Gratias, J.W. Cahn, Phys. Rev. Lett. 53, 1951 (1984) Google Scholar
  2. R. Merlin, K. Bajema, R. Clarke, F.-Y. Juang, P.K. Battacharya, Phys. Rev. Lett. 55, 1768 (1985) Google Scholar
  3. Q. Niu, F. Nori, Phys. Rev. B 42, 10329 (1990) Google Scholar
  4. Y. Liu, W. Strakool, Phys. Rev. B 43, 1110 (1991) Google Scholar
  5. N. Fujita, K. Niizeki, Phys. Rev. B 64, 144207 (2001) Google Scholar
  6. M. Komoto, L.P. Kadanoff, C. Tang, Phys. Rev. Lett. 50, 1870 (1983) Google Scholar
  7. V. Kumar, G. Ananthakrishna, Phys. Rev. Lett. 59, 1476 (1987) Google Scholar
  8. X.Q. Huang, C.D. Gong, Phys. Rev. B 58, 739 (1998) Google Scholar
  9. E. Macia, F. Dominguez-Adame, Phys. Rev. Lett. 76, 2957 (1996) Google Scholar
  10. E.L. Albuquerque, M.G. Cottam, Phys. Rep. 376, 225 (2003) Google Scholar
  11. E. Macia, Rep. Prog. Phys. 69, 397 (2006) Google Scholar
  12. S. Chattopadhyay, A. Chakrabarti, Phys. Rev. B 65, 184204 (2002) Google Scholar
  13. M. Naka, K. Ino, M. Kohmoto, Phys. Rev. B 71, 245120 (2005) Google Scholar
  14. D. Jin, G. Jin, Phys. Rev. B 71, 014212 (2005) Google Scholar
  15. M. Dinu, D.D. Nolte, M.R. Melloch, Phys. Rev. B 56, 1987 (1997) Google Scholar
  16. J.E. Zarate, V.R. Velasco, Phys. Rev. B 65, 045304 (2001) Google Scholar
  17. P.W. Anderson, Phys. Rev. 109, 1492 (1958) Google Scholar
  18. P. Phillips, H.-L. Wu, Science 252, 1805 (1991) Google Scholar
  19. J.C. Flores, J. Phys.: Condens. Matter 1, 8471 (1989) Google Scholar
  20. W. Kim, L. Covaci, F. Marsiglio, Phys. Rev. B 73, 195109 (2006) Google Scholar
  21. F.A.B.F. de Moura, M. Lyra, Phys. Rev. Lett. 81, 3735 (1998) Google Scholar
  22. F.M. Izrailev, A.A. Krokhin, Phys. Rev. Lett. 82, 4062 (1997) Google Scholar
  23. M. Hilke, J.C. Flores, Phys. Rev. B 55, 10625 (1997) Google Scholar
  24. D. Huang, Phys. Rev. B 70, 205124 (2004) Google Scholar
  25. A. Esmailpour, M. Esmaeilzadeh, E. Faizabadi, P. Carpena, M.R.R. Tabar, Phys. Rev. B 74, 024206 (2004) Google Scholar
  26. M. Stęślicka, R. Kucharczyk, A. Akjouj, B. Djafari-Rouhani, L. Dobrzynski, S.G. Davison, Surf. Sci. Rep. 47, 93 (2002) Google Scholar
  27. W.J. Hsueh, H.C. Chen, Phys. Rev. E 76, 057701 (2007) Google Scholar
  28. C.L. Roy, A. Khan, Phys. Rev. B 49, 14979 (1994) Google Scholar
  29. P. Panchadhyayee, R. Biswas, A. Khan, P.K. Mahapatra, J. Phys.: Condens. Matter 20, 275243 (2008) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Engineering ScienceNational Taiwan UniversityTaipeiTaiwan

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