Magnetotransport in a Two-Dimensional Electron Gas Subject to a Weak Superlattice Potential

  • R. R. Gerhardts
  • D. Pfannkuche
  • D. Weiss
  • U. Wulf
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 101)


We present experimental and theoretical results on commensurability oscillations of the magnetoresistivity in high-mobility two-dimensional electron systems subject to a weak superlattice potential. Experimentally, the band conductivity of a sample with a hologra-phically produced square-grid potential is shown to be considerably smaller than that of the same sample with a similar linear grating potential of the same lattice constant. This is explained by a magnetotransport theory with due consideration of collision broadening effects and the peculiar subband splitting of Landau levels resulting in a Hofstadter-type energy spectrum.


Band Conductivity Landau Level Flat Band Perpendicular Magnetic Field Grid Modulation 
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  1. [1]
    C.G. Smith, M. Pepper, R. Newbury, H. Ahmed, D.G. Hasko, D.C. Peacock, J.E.F. Frost, D.A. Ritchie, G.A.C. Jones, and G. Hill, J. Phys.: Condensed Matter 2, 3405 (1990).CrossRefGoogle Scholar
  2. [2]
    D. Weiss, K. v. Klitzing, K. Ploog, and G. Weimann, Europhys. Lett. 8, 179 (1989) see also in High Magnetic Fields in Semiconductor Physics II, edited by G. Landwehr, Springer Series in Solid-State Sciences Vol. 87 (Springer-Verlag, Berlin 1989), p. 357.CrossRefGoogle Scholar
  3. [3]
    R.R. Gerhardts, D. Weiss, and K. v. Klitzing, Phys. Rev. Lett. 62, 1173 (1989).CrossRefGoogle Scholar
  4. [4]
    R.W. Winkler, J.P. Kotthaus, and K. Ploog, Phys. Rev. Lett. 62, 1177 (1989).CrossRefGoogle Scholar
  5. [5]
    R.R Gerhardts, in Science and Engineering of One-and Zero-Dimensional Semiconductors, ed. by S.P. Beaumont and C.M. Sotomajor Torres (Plenum Press, New York, 1990), p. 231.Google Scholar
  6. [6]
    C.W.J. Beenakker, Phys. Rev. Lett. 62, 2020 (1989).CrossRefGoogle Scholar
  7. [7]
    R.R. Gerhardts and C. Zhang, Phys. Rev. Lett. 64, 1473 (1990).CrossRefGoogle Scholar
  8. R.R. Gerhardts and C. Zhang, Surf. Sci. 229, 92 (1990).CrossRefGoogle Scholar
  9. [8]
    C. Zhang and R.R. Gerhardts, Phys. Rev. B 41, 12850 (1990).CrossRefGoogle Scholar
  10. [9]
    M.Y. Azbel’, Sov. Phys. JETP 19, 634 (1964).Google Scholar
  11. M. Ya. Azbel’, [Zh. Eksp. Teor. Fiz. 46, 929 (1964)].Google Scholar
  12. [10]
    R.D. Hofstadter, Phys. Rev. B 14, 2239 (1976).CrossRefGoogle Scholar
  13. [11]
    A. Rauh, phys. stat. sol. (b) 69, K9 (1975).CrossRefGoogle Scholar
  14. [12]
    For a recent review see: D.J. Thouless, in The Quantum Hall Effect, edited by R.E. Prange and S.M. Girvin (Springer-Verlag, New York, 1987).Google Scholar
  15. [13]
    N.A. Usov Sov. Phys. JETP 67 2565 1988Google Scholar
  16. N.A. Usov, [Zh. Eksp. Teor. Fiz. 94, 305 (1988)].Google Scholar
  17. [14]
    The sample is considered as a part of an infinitely extended system. The plane waves are normalized on a length L y, the øn on the total x-axis. To count states correctly, x 0 is considered within a length L x taken as a suitable (B-dependent) multiple of the period a. Finally, the limit L x, L y → ∞ is taken.Google Scholar
  18. [15]
    D. Weiss, C. Zhang, R.R. Gerhardts, K. v. Klitzing, and G. Weimann, Phys. Rev. B 39, 13020 (1989).CrossRefGoogle Scholar
  19. [16]
    T. Ando, A.B. Fowler, and F. Stern, Rev. Mod. Phys. 54, 437 (1982).CrossRefGoogle Scholar
  20. [17]
    For computational convenience, the plots are calculated using the approximation A n α(E) = (2πГ2)−½ exp[−(EE n )2/2Г2]Google Scholar
  21. [18]
    G. Czycholl and W. Ponischowski, Z. Physik B.— Cond. Matter 73, 343 (1988).CrossRefGoogle Scholar
  22. [19]
    See, e.g., R.R. Gerhardts, Z. Phys. B 22, 327 (1975).CrossRefGoogle Scholar
  23. [20]
    If one replaces, in the spirit of Eq.(ll), the factor […]2 in Eq.(14) by 2l 2Г0 D n(E), one gets the n-independent scattering rate Гn = 2Г0, and σsc xx reduces to Eq.(9) of Ref.21, where Г0 is written as (N 1U2 0/2πl 2)/Г One thus misses the leading order contribution to the oscillations of ρyy, retaining higher order contributions with small amplitudes of the order.Google Scholar
  24. [21]
    P. Vasilopoulos and F.M. Peeters, Phys. Rev. Lett. 63, 2120 (1989).CrossRefGoogle Scholar
  25. [22]
    P. Streda and A.H MacDonald, Phys. Rev. B 41, 11 892 (1990).Google Scholar
  26. [23]
    U. Wulf, V. Gudmundsson, and R.R. Gerhardts, Phys. Rev. B 38, 4218 (1988).CrossRefGoogle Scholar
  27. V. Gudmundsson and R.R. Gerhardts, Phys. Rev. B 35, 8005 (1987).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • R. R. Gerhardts
    • 1
  • D. Pfannkuche
    • 1
  • D. Weiss
    • 1
  • U. Wulf
    • 1
  1. 1.Max-Planck-Institut für FestkörperforschungStuttgart 80Germany

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