Skip to main content

Quantum transport in thin films and inversion layers

  • Chapter
  • First Online:
Festkörperprobleme 30

Part of the book series: Advances in Solid State Physics ((ASSP,volume 30))

Abstract

A variety of quantum effects in the low temperature transport properties of thin metallic films and inversion layers were discovered during the past decade. Examples are the quantized Hall effect observed in inversion layers subject to a strong perpendicular magnetic field, the quantum interference (Aharonov-Bohm-like) oscillations of the magnetoresistance of thin, normal metallic cylinders, and the so-called universal conductance fluctuations in mesoscopic samples. Most recently, conductance quantization was reported in quasi-ballistic inversion layers in AlGaAs/GaAs-heterostructures even without magnetic field. Several frequency and time dependent as well as non-linear mesoscopic phenomena were predicted. In this article the physical background of some of the effects is described, and the corresponding theory is outlined.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.Ya Azbel, A. Hartstein, and D.P. Di Vicenzo, Europhysics News 15, 3 (1984).

    Google Scholar 

  2. S. Washburn and R.A. Webb, Adv. Phys. 35, 375 (1986)

    Article  ADS  Google Scholar 

  3. H. Heinrich, G. Bauer, and F. Kuchar, eds., Physics and Technology of Submicron Devices, Springer Ser. Sol. St. Sciences 83, (Springer Verlag, Berlin, Heidelberg, New York 1988)

    Google Scholar 

  4. E. Abrahams, P.W. Anderson, D.C. Licciardello, and T.V. Ramakrishnan, Phys. Rev. Letters 42 673 (1979)

    Article  ADS  Google Scholar 

  5. L.P. Gorkov, A.I. Larkin, and D.E. Khmel'nitskii, Sov. Phys. JETP Letters 30, 228 (1979)

    ADS  Google Scholar 

  6. D. Vollhardt and P. Wölfle, Phys. Rev. Letters 45, 842 (1980); Phys. Rev. B 22, 4666 (1980)

    Article  ADS  Google Scholar 

  7. S. Hikami, A.I. Larkin, and Y. Nagaoka, Progr. Theor. Phys. 63, 707 (1980)

    Article  ADS  Google Scholar 

  8. B.L. Altshuler, D. Khmel'nitskii, A.I. Larkin, and P.A. Lee, Phys. Rev. B 22, 5142 (1980)

    Article  ADS  Google Scholar 

  9. P.A. Lee and T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985)

    Article  ADS  Google Scholar 

  10. G. Bergmann, Phys. Rep. 107, 1 (1984)

    Article  ADS  Google Scholar 

  11. B. Kramer, G. Bergmann, and Y. Bruynseraede, eds., Localization Interaction, and Transport Phenomena, Springer Ser. Sol. St. Sci. 61 (Springer Verlag, Berlin, Heidelberg, New York 1985)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  13. D.C. Tsui, H.L. Störmer, and A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)

    Article  ADS  Google Scholar 

  14. K. von Klitzing, Rev. Mod. Phys. 58, 519 (1986)

    Article  ADS  Google Scholar 

  15. E. Prange and S. Girvin, eds., The Quantum Hall Effect, (Springer Verlag, Berlin, Heidelberg, New York 1987)

    Google Scholar 

  16. M.A. Paalanen, D.C. Tsui, and A.C. Gossard, Phys. Rev. Lett. 25, 5566 (1982)

    ADS  Google Scholar 

  17. A.M. Chang, P. Berglund, D.C. Tsui, H.L. Störmer, and J.C.M. Hwang, Phys. Rev. Lett. 53, 997 (1984)

    Article  ADS  Google Scholar 

  18. B.L. Altshuler, A.G. Aronov, and B.Z. Spivak, JETP Letters 33, 94 (1981)

    ADS  Google Scholar 

  19. D.Yu. Sharvin and Yu.V. Sharvin, JETP Letters 34, 272 (1981)

    ADS  Google Scholar 

  20. M. Gijs, C. Van Haesendonck, and Y. Bruynseraede, Phys. Rev. Lett. 52, 2069 (1984)

    Article  ADS  Google Scholar 

  21. B. Pannetier, J. Chaussy, R. Rammal, and P. Gandit, Phys. Rev. Lett. 53, 718 (1984)

    Article  ADS  Google Scholar 

  22. A.G. Aronov and Yu.V. Sharvin, Rev. Mod. Phys. 59, 755 (1987)

    Article  ADS  Google Scholar 

  23. A.B. Fowler, A. Hartstein, and R.A. Webb, Phys. Rev. Lett. 48, 196 (1982)

    Article  ADS  Google Scholar 

  24. A.B. Fowler, J.J. Wainer, and R.A. Webb, IBM J. Res. Develop. 32, 372 (1988)

    Article  Google Scholar 

  25. B.L. Altshuler, Sov. Phys. JETP Letters 41, 649 (1985)

    ADS  Google Scholar 

  26. P.A. Lee and A.D. Stone, Phys. Rev. Lett. 55, 1622 (1985).

    Article  ADS  Google Scholar 

  27. P.A. Lee, A.D. Stone, and H. Fukuyama, Phys. Rev. B 35, 94 (1987)

    Google Scholar 

  28. J.L. Pichard and M. Sanquer, in: Proc. Int. Workshop on the Anderson Transition and Mesoscopic Fluctuations, Braunschweig, (1990), Physica, in press (1990)

    Google Scholar 

  29. B.J. van Wees, L.P. Kouwenhoven, H. van Houten, C.W.J. Beenakker, J.E. Mooij, C.T. Foxon, and J.J. Harris, Phys. Rev. B 38, 3525 (1988); B. J. van Wees, H. van Houten, C.W.J. Beenakker, J.G. Williamson, L.P. Kouwenhoven, D. van der Marel, and C.T. Foxon, Phys. Rev. lett. 60, 848 (1988)

    Article  Google Scholar 

  30. D.A. Wharam, T.J. Thornton, R. Newbury, M. Pepper, A. Ahmed, J.E.F. Frost, D.G. Hasko, D.C. Peacock, D.A. Ritchie, and G.A.C. Jones, J. Phys. C 21, L209 (1987)

    Article  Google Scholar 

  31. A.D. Benoit, C.P. Umbach, R.B. Laibowitz, and R.A. Webb, Phys. Rev. Lett. 58, 2343 (1987)

    Article  ADS  Google Scholar 

  32. H.U. Baranger, A.D. Stone, and D.P. Di Vincenzo, Phys. Rev. B 37, 6521 (1988)

    Article  ADS  Google Scholar 

  33. R.A. Webb, S. Washburn, J.H. Haube, A.D. Benoit, C.P. Umbach, and F.P. Millikan, in Ref. [3], p. 98.

    Google Scholar 

  34. M. Büttiker, Y. Imry, and R. Landauer, Phys. Lett. 96 A, 365 (1983)

    ADS  Google Scholar 

  35. M. Büttiker, Phys. Rev. B 32, 1846 (1985)

    Article  ADS  Google Scholar 

  36. H.F. Cheung, Y. Gefen, E.K. Riedel, and W.H. Shih, Phys. Rev. B 37, (1988)

    Google Scholar 

  37. Ho-Fai Chung, Y. Genen, and E.K. Riedel, IBM J. Res. Dev. 32, 359 (1988)

    Article  Google Scholar 

  38. B.L. Altshuler, V.E. Kravtsov, and I.V. Lerner, Pi'ma Zh. Exp. Teor. Fiz. 45, 160 (1987)

    Google Scholar 

  39. B.L. Altshuler, V.E. Kravtsov, and I.V. Lerner, in: Anderson Localization, ed. by T. Ando and H. Fukuyama, Springer Proc. Phys. 28, 300, (Springer Verlag, Berlin, Heidelberg New York 1988); Sov. Phys. JETP 67, 795 (1988)

    Google Scholar 

  40. A. Ludviksson, R. Kree, and A. Schmid, Phys. Rev. Lett. 52, 950 (1984)

    Article  ADS  Google Scholar 

  41. P. Sheng, Z.-Q. Zhang, B. White, and G. Papanicolaou, Phys. Rev. Lett. 57, 1000 (1986)

    Article  ADS  Google Scholar 

  42. S. Feng, P.A. Lee, and A.D. Stone, Phys. Rev. Lett. 58, 1960 (1987)

    Article  Google Scholar 

  43. N.O. Birge, B. Golding, and W.H. Haemmerle, Phys. Rev. Lett. 62, 195 (1989)

    Article  ADS  Google Scholar 

  44. D.E. Khmel'nitskii, in: Anderson Localization, ed. by T. Ando and H. Fukuyama, Springer Proc. Phys. 28, 323, (Springer Verlag, Berlin, Heidelberg, New York 1988)

    Google Scholar 

  45. V. Fal'ko, Europhys. Letters 8, 785 (1989)

    Article  ADS  Google Scholar 

  46. J. Masek and B. Kramer, Sol. St. Commun. 68, 611 (1988); Z. Phys. B 75, 37 (1989)

    Article  ADS  Google Scholar 

  47. D.E. Khmel'nitskii, in [51] For most recent results see Proc. 6th Int. Winterschool in Sol. St. Phys., Mauterndorf, Springer Series in Solid State Sciences, ed. by F. Kuchar, H. Heinrich, and G. Bauer (1990)

    Google Scholar 

  48. B.L. Altshuler and A.G. Aronov, in: Electron-Electron Interactions in Disordered Systems, ed. by A.L. Efros and M. Pollak, 1 North Holland (1985)

    Google Scholar 

  49. H. Fukuyama, ibid. in: Electron-Electron Interactions in Disordered Systems, ed. by A.L. Efros and M. Pollak, 1 North Holland (1985) 155

    Google Scholar 

  50. K. von Klitzing, this volume

    Google Scholar 

  51. For most recent results see Proc. 6th Int. Winterschool in Sol. St. Phys., Mauterndorf, Springer Series in Solid State Sciences, ed. by F. Kuchar, H. Heinrich, and G. Bauer (1990)

    Google Scholar 

  52. D.J. Thouless, Phys. Rev. Lett. 39, 1167 (1977)

    Article  ADS  Google Scholar 

  53. D.J. Thouless, Sol. St. Commun. 34, 683 (1980)

    Article  ADS  Google Scholar 

  54. P.W. Anderson, E. Abrahams, and T.V. Ramakrishnan, Phys. Rev. Lett. 43, 718 (1979)

    Article  ADS  Google Scholar 

  55. N.F. Mott and E.A. Davis, Electronic Processes in Non-Crystalline Materials, (Clarendon Press, Oxford 1971)

    Google Scholar 

  56. F.P. Milliken, S. Washburn, C.P. Umbach, R.B. Laibowitz, and R.A. Webb, Phys. Rev. B 36, 4465 (1987)

    Article  ADS  Google Scholar 

  57. D.S. Fisber and P.A. Lee, Phys. Rev. B 23, 6851 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  58. A.D. Stone and A. Szafer, IBM J. Res. Develop. 32, 384 (1988)

    Article  Google Scholar 

  59. V.E. Kravtsov and I.V. Lerner, Sol. St. Commun. 52, 593 (1984)

    Article  ADS  Google Scholar 

  60. B. Shapiro, Phys. Rev. B 34, 4394 (1986)

    Article  ADS  Google Scholar 

  61. K.S. Chase and A. Mac Kinnon, J. Phys. C 20, 6189 (1987)

    Article  ADS  Google Scholar 

  62. M. Schreiber and B. Kramer, in: The Physics of Semiconductors, ed. by W. Zawadzki, Vol. 1, 87 Polish Acad. Sci., Warsaw (1988)

    Google Scholar 

  63. M. Büttiker, this volume

    Google Scholar 

  64. B. Velicky, J. Masek, and B. Kramer, Phys. Lett. 140, 447 (1989)

    Article  Google Scholar 

  65. Y. Isawa, J. Phys. Soc. Japan 57, 3457 (1988)

    Article  ADS  Google Scholar 

  66. R. Johnston and L. Schweitzer, J. Phys. C 21, L861 (1988)

    Article  ADS  Google Scholar 

  67. G. Kirczenov, Phys. Rev. Lett. 62, 1920 (1989)

    Article  ADS  Google Scholar 

  68. A. Szafer and A.D. Stone, Phys. Rev. Lett. 62, 300 (1989)

    Article  ADS  Google Scholar 

  69. A. Kawabata, J. Phys. Soc. Japan 58, 372 (1989)

    Article  ADS  Google Scholar 

  70. L.I. Glazman, G.B. Lesovik, D.E. Khmel'nitskii, and R.I. Shekhter, JETP Letters 48, 239 (1988)

    ADS  Google Scholar 

  71. G. Ebert, K. von Klitzing, C. Probst, and K. Ploog, Sol. St. Commun. 44, 95 (1982)

    Article  ADS  Google Scholar 

  72. H.P. Wei, D.C. Tsui, M.A. Paalanen, and A.M.M. Pruisken, Phys. Rev. Lett. 61, 1294 (1988)

    Article  ADS  Google Scholar 

  73. H.P. Wei, S.W. Hwang, D.C. Tsui, and A.M.M. Pruisken, Proc. EP2DS8, Grenoble, Surf. Sci. (1990), in press

    Google Scholar 

  74. L. Engel, H.P. Wei, D.C. Tsui, and M. Shayegan, Proc. EP2DS8, Grenoble, Surf. Sci. (1989), in press

    Google Scholar 

  75. R.G. Clark, S.R. Haynes, J.V. Branch, J.R. Mallet, A.M. Suckling, PA. Wright, P.M.W. Oswald, J.J. Harris, and C.T. Foxon, Proc. EP2DS8, Grenoble, Surf. Sci. (1990), in press

    Google Scholar 

  76. J.V. Branch, R.G. Clark, C. Andrikidis, S.J. Collocott, G.J. Griffiths, J.J. Harris C.T. Foxon, and J.T. Chalker, (1990), to be published

    Google Scholar 

  77. K.Y. Lim, I. Auer, F. Kuchar, G. Weimann, W. Schlapp, and A. Forchel, in: Proc. EP2DS8, Grenoble, Surf. Sci. (1990), in press

    Google Scholar 

  78. W. Möhle, H. Adrian, L. Bliek, G. Weimann, and W. Schlapp, Superlattices & Microstructures 5, 465 (1989)

    Article  ADS  Google Scholar 

  79. L.A. Galchenkov, I.M. Grodnenskii, M.V. Kostovestkii, and O.R. Matov, JETP Letters 46, 542 (1987); F. Kuchar, private communication

    ADS  Google Scholar 

  80. H. Aoki, Rep. Progr. Phys. 50, 655 (1987)

    Article  ADS  Google Scholar 

  81. J.K. Jain, S.A. Kivelson, and N. Trivedi, Phys. Rev. Lett. 64, 1297 (1990)

    Article  ADS  Google Scholar 

  82. B. Huckestein and B. Kramer, Sol. St. Commun. 71, 445 (1989); Phys. Rev. Lett. 64, 1437 (1990)

    Article  ADS  Google Scholar 

  83. B. Huckestein, W. Apel, and B. Kramer, in [51] For most recent results see Proc. 6th Int. Winterschool in Sol. St. Phys., Mauterndorf, Springer Series in Solid State Sciences, ed. by F. Kuchar, H. Heinrich, and G. Bauer (1990)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ulrich Rössler

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH

About this chapter

Cite this chapter

Kramer, B. (1990). Quantum transport in thin films and inversion layers. In: Rössler, U. (eds) Festkörperprobleme 30. Advances in Solid State Physics, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0108282

Download citation

  • DOI: https://doi.org/10.1007/BFb0108282

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-528-08038-9

  • Online ISBN: 978-3-540-75346-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics