Skip to main content
SpringerLink
Log in

Microwave investigations of the quantum hall effect in GaAs/AlGaAs heterostructures

  • Chapter
  • First Online:
Festkörperprobleme 28

Part of the book series: Advances in Solid State Physics ((ASSP,volume 28))

Abstract

Microwave Hall effect experiments confirm the d.c. results regarding the integral quantum Hall effect (IQHE). They also give additional information on the intrinsic plateau width in σxy, on the behavior at the spin resonance, and on the importance of sample edges, as well as an indication for the breakdown of the IQHE at frequencies lower than the cyclotron resonance frequency. The numerical value of the microwave Hall conductivity on the i=4 plateau agrees with the value obtained from the d.c. Hall resistance. Experiments on micron-size structures demonstrate that the Hall effect in particular the IQHE can be measured on “small” samples without potential probes perturbing the low-dimensionality of the electron gas.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. See e.g. the review by F. Koch, in: Festkörperproblem/Advances in Solid State Physics XV, ed. by H. J. Queisser (Pergamon, Vieweg, Braunschweig 1975), p. 79

    Google Scholar 

  2. W. Hansen, J. P. Kotthaus, A. Chaplik, and K. Ploog, in: High Magnetic Fields in Semiconductor Physics, Proc. of the Int. Conf. Würzburg 1986, ed. by G. Landwehr (Springer, Berlin 1987), p. 266; W. Hansen PhD Thesis, University of Hamburg 1987

    Google Scholar 

  3. K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett 45, 494 (1980)

    Article  ADS  Google Scholar 

  4. F. Kuchar, R. Meisels, G. Weimann, and W. Schlapp, Phys. Rev. B33, 2965 (1986)

    Article  ADS  Google Scholar 

  5. V. A. Volkov, D. V. Galchenkov, L. A. Galchenkov, I. M. Grodnenskii, O. R. Matov, S. A. Mikhailov, A. P. Senichkin, and K. V. Starostin, JETP Lett. 43, 328 (1986) [russian original: Pis'ma Zh. Eksp. Teor. Fiz. 43, 255 (1986)]

    ADS  Google Scholar 

  6. Y. Ono, in: Anderson Localization, ed. by Y. Nagaoka and H. Fukuyama (Springer, Berlin, Heidelberg, New York 1982), p. 207; Y. Ono, Prog. Theor. Phys., Suppl. 84, 138 (1985)

    Google Scholar 

  7. R. Joynt, J. Phys. C18, L331 (1985)

    Article  ADS  Google Scholar 

  8. R. Willett, H. L. Störmer, D. C. Tsui, A. C. Gossard, J. H. English, and K. W. Baldwin, Surf. Sci. 196, 257 (1988)

    Article  ADS  Google Scholar 

  9. F. Kuchar, R. Meisels, K. Y. Lim, P. Pichler, G. Weimann, and W. Schlapp, Physica Scripta T19A, 79 (1987); F. Kuchar, R. Meisels, K. Y. Lim, P. Pichler, G. Weimann, and W. Schlapp, in: High Magnetic Fields in Semiconductor Physics, Proc. of the Int. Conf. Würzburg 1986, ed. by G. Landwehr (Springer, Berlin 1987), p. 95

    Article  ADS  Google Scholar 

  10. B. B. Goldberg, T. P. Smith, M. Heiblum, and P. J. Stiles, Surface Science 170, 180 (1986)

    Article  ADS  Google Scholar 

  11. R. Meisels, K. Y. Lim, F. Kuchar, G. Weimann, and W. Schlapp, in: Two-dimensional Systems: Physics and New Devices, ed. by G. Bauer, F. Kuchar, H. Heinrich (Springer, Berlin, Heidelberg 1986), p. 184

    Google Scholar 

  12. G. L. Ragan, Microwave Transmission Circuits (McGraw-Hill, New York, Toronto, Lodon 1948), p. 46

    Google Scholar 

  13. Further details of the calculation can be found in: R. Meisels and F. Kuchar, Z. Phys. 67, 443 (1987)

    Article  Google Scholar 

  14. G. Weimann and W. Schlapp, Appl. Phys. A37, 3057 (1985)

    Article  Google Scholar 

  15. D. Stein, K. v. Klitzing, and G. Weimann, Phys. Rev. Letters 51, 130 (1983)

    Article  ADS  Google Scholar 

  16. R. Meisels, F. Kuchar, K. Y. Lim, G. Weimann, and W. Schlapp, Surf. Sci. 196, 177 (1988)

    Article  ADS  Google Scholar 

  17. G. Ebert, K. v. Klitzing, and G. Weimann, J. Phys. C18, L257 (1985)

    Article  ADS  Google Scholar 

  18. H. Z. Zheng, D. C. Tsui, and A. M. Chang, Phys. Rev. B32, 550 (1985)

    Article  ADS  Google Scholar 

  19. R. Woltjer, R. Eppenga, and M. F. H. Schuurmans, in: High Magnetic Fields in Semiconductor Physics, Proc. of the Int. Conf. Würzburg 1986, ed. by G. Landwehr (Springer, Berlin 1987), p. 104

    Google Scholar 

  20. J. P. Kotthaus, Physica Scripta T19A, 120 (1987)

    Article  ADS  Google Scholar 

  21. G. Timp, A. M. Chang, P. de Vegvar, R. E. Howard, R. Behringer, J. E. Cunningham, and P. Mankiewich, Surf. Sci. 196, 68 (1988)

    Article  ADS  Google Scholar 

  22. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York 1941)

    MATH  Google Scholar 

  23. E. C. Stoner, Phil. Mag. 36, 803 (1945)

    Google Scholar 

  24. J. A. Osborn, Phys. Rev. 67, 351 (1945)

    Article  ADS  Google Scholar 

  25. S. J. Allen, Jr., H. L. Störmer, and J. C. M. Hwang, Phys. Rev. B28, 4875 (1983)

    Article  ADS  Google Scholar 

  26. S. A. Govorkov, M. I. Reznikov, A. P. Senichkin, and V. I. Talyanskii, JETP Letters 44, 487 (1986)

    ADS  Google Scholar 

  27. S. J. Allen, F. DeRosa, G. J. Dolan, and C. W. Tu, Proc. 17th IPCS, San Francisco 1984, ed. by J. D. Chadi and W. A. Harrison (Springer, New York 1985), p. 313

    Google Scholar 

  28. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York 1965), p. 591

    Google Scholar 

  29. R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, Phys. Rev. B8, 3689 (1973)

    Article  ADS  Google Scholar 

  30. R. F. Kazarinov and S. Luryi, Phys. Rev. B25, 7626 (1982)

    Article  ADS  Google Scholar 

  31. S. M. Apenko and Yu. E. Lozovik, J. Phys. C18, 1197 (1985)

    Article  ADS  Google Scholar 

  32. B. I. Halperin, Phys. Rev. B25, 2185 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  33. R. Rammal, G. Toulouse, M. T. Jaekel, and B. I. Halperin, Phys. Rev. B27, 5142 (1983)

    Article  ADS  Google Scholar 

  34. A. H. MacDonald and P. Streda, Phys. Rev. B29, 1616 (1984)

    Article  ADS  Google Scholar 

  35. B. Kramer, in: High Magnetic Fields in Semiconductor Physics, ed. by G. Landwehr, Proc. of the Int. Conf. Würzburg, 1986 (Springer, Berlin 1987), p. 33

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Festkörperphysik der Universität Wien, A-1090, Wien, Austria

    Friedl Kuchar

  2. Ludwig Boltzmann Institut für Festkörperphysik, Kopernikusgasse 15, A-1060, Wien, Austria

    Friedl Kuchar

Authors
  1. Friedl Kuchar
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

U. Rössler

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH

About this chapter

Cite this chapter

Kuchar, F. (1988). Microwave investigations of the quantum hall effect in GaAs/AlGaAs heterostructures. In: Rössler, U. (eds) Festkörperprobleme 28. Advances in Solid State Physics, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107847

Download citation

  • DOI: https://doi.org/10.1007/BFb0107847

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-528-08034-1

  • Online ISBN: 978-3-540-75352-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation