Skip to main content
SpringerLink
Log in

The Shubnikov-de Haas Effect and Quantum-Limit Phenomena in Semiconductors

  • Chapter
Physics of Solids in Intense Magnetic Fields

Abstract

In 1930 Shubnikov and de Haas (1) investigated the magnetoresistance of bismuth single crystals at liquid hydrogen temperatures. They observed an oscillatory behavior of the resistance as a function of the magnetic field which was not understood at that time. The foundation for the explanation was laid by Landau (2). Peierls (3) suggested in 1931 that quantum effects might cause the phenomenon. However, not too much attention was paid to the effect, possibly because knowledge of the peculiar behavior was restricted to bismuth for quite some time. Not until 1956 was an oscillatory magnetoresistance, which is now frequently called the Shubnikov-de Haas effect, observed in other substances, in the semiconductor InSb (4) and in Zn (5). Soon experiments on InAs (6,7) followed, and to the present the Shubnikov-de Haas effect has been found in more than a dozen semiconductors. At the end of the 1950’s the first quantitative theories were offered (8–10) which showed much similarity with the theory of the de Haas-Van Alphen effect. Excellent review articles by Kahn and Frederikse (11) and by Adams and Keyes (12) have been published which cover the literature up to about 1961. Consequently, in this chapter emphasis will be on the newer results. In the first section, on oscillatory quantum effects, the theoretical situation will briefly be reviewed, followed by a presentation of recent experimental data.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Shubnikov and W. J. de Haas, Nature 126: 500 (1930).

    Article  ADS  Google Scholar 

  2. L. D. Landau, Z. Phys. 64: 629 (1930).

    Article  ADS  MATH  Google Scholar 

  3. R. Peierls, Z. Phys. 81: 186 (1933).

    Article  ADS  MATH  Google Scholar 

  4. H. P. R. Frederikse and W. R. Hosier, Can. J. Phys. 34: 1377 (1956).

    Article  ADS  Google Scholar 

  5. P. B. Alers, Phys. Rev. 101. 41 (1956).

    Article  ADS  Google Scholar 

  6. R. Sladek, Phys. Rev. 110: 817 (1958).

    Article  ADS  Google Scholar 

  7. H. P. R. Frederikse and W. R. Hosler, Phys. Rev. 110: 880 (1958).

    Article  ADS  Google Scholar 

  8. P. N. Argyres, Phys. Rev. 109: 1115 (1958).

    Article  ADS  Google Scholar 

  9. I. M. Lifshitz, Phys. Chem. Solids 4: 11 (1958).

    Article  ADS  Google Scholar 

  10. E. N. Adams and T. D. Holstein, J. Phys. Chem. Solids 10: 254 (1959).

    Article  ADS  Google Scholar 

  11. A. H. Kahn and H. P. R. Frederikse, in: Solid State Physics, Vol. 9 (F. Seitz and D. Turnbull, eds.), Academic Press, New York and London, 1959, p. 257.

    Google Scholar 

  12. E. N. Adams and R. W. Keyes, Progress in Semiconductors, Vol. 6, (A. F. Gibson, ed.), Heywood & Co., London, 1962.

    Google Scholar 

  13. R. Kubo, S. J. Miyake, and N. Hashitsume, Solid State Physics, Vol. 17 (F. Seitz and D. Turnbull, eds.), Academic Press, New York and London, 1965f.

    Google Scholar 

  14. L. Onsager, Phil. Mag. 43: 1006 (1952).

    Google Scholar 

  15. G. E. Smith, G. A. Baraff, and J. M. Rowell, Phys. Rev. 135: A1118 (1964).

    Article  ADS  Google Scholar 

  16. E. N. Adams, Phys. Rev. 85: 41 (1952).

    Article  ADS  MATH  Google Scholar 

  17. D. E. Soule, J. W. McClure, and L. B. Smith, Phys. Rev. 134: A453 (1964).

    Article  ADS  Google Scholar 

  18. P. N. Argyres, J. Phys. Chem. Solids 4: 19 (1958).

    Article  ADS  Google Scholar 

  19. R. B. Dingle, Proc. Roy. Soc. A211: 517 (1952).

    Article  ADS  Google Scholar 

  20. J. W. McClure, Phys. Rev. 112: 715 (1958).

    Article  ADS  Google Scholar 

  21. A. H. Kahn, Phys. Rev. 119: 1189 (1960).

    Article  ADS  MATH  Google Scholar 

  22. L. S. Lerner, Phys. Rev. 127: 1480 (1962).

    Article  ADS  Google Scholar 

  23. L. S. Lerner, Phys. Rev. 130: 605 (1963).

    Article  ADS  Google Scholar 

  24. J. B. Ketterson and Y. Eckstein, Phys. Rev. 132: 1885 (1963); Phys. Rev. 137: A1777 (1965).

    Article  ADS  Google Scholar 

  25. R. D. Brown, IBM J. Res. Develop. 10: 462 (1966).

    Article  Google Scholar 

  26. Kh. I. Amirkhanov, R. I. Bashirov and Yn. E. Zakiev, Soviet Phys.—Solid State (English Transl.) 5: 340 (1963).

    Google Scholar 

  27. M. S. Bresler, R. V. Parfen’ev, and S. S. Shalyt, Soviet Phys. - Solid State (English Transl.) 7: 1025 (1965); 8: 1414 (1966).

    Google Scholar 

  28. Kh. I. Amirkhanov and R. I. Bashirov, Soviet Phys.-JETP Letters (English Transl.) 1: 49 (1965).

    ADS  Google Scholar 

  29. A. L. Efros, Soviet Phys.—Solid State (English Transl.) 7: 1206 (1965).

    Google Scholar 

  30. L. E. Gurevich and A. L. Efros, Soviet Phys.—JETP (English Transl.) 16: 402 (1963).

    ADS  Google Scholar 

  31. G. A. Antcliffe and R. A. Stradling, Phys. Letters 20: 119 (1966).

    Article  ADS  Google Scholar 

  32. M. S. Bresler, N. A. Redko, and S. S. Shalyt, Phys. Stat. Sol. 15: 745 (1966).

    Article  ADS  Google Scholar 

  33. W. M. Becker and H. Y. Fan, in:Proceedings of the International Conference on the Physics of Semiconductors, Paris, 1964, Dunod, Paris, 1964, p. 663.

    Google Scholar 

  34. T. O. Yep and W. M. Becker, Phys. Rev. 144: 741 (1966);

    Article  ADS  Google Scholar 

  35. T. O. Yep and W. M. Becker, Phys. Rev. 156: 939 (1967).

    Article  ADS  Google Scholar 

  36. I. G. Fakidov and E. A. Zavadskii, Soviet Phys.—JETP (English Transl.) 4: 716 (1958).

    Google Scholar 

  37. W. Bernard, H. Roth, W. D. Straub, and J. E. Mulhern, Phys. Rev. 135: A1386 (1964).

    Article  ADS  Google Scholar 

  38. E. Braun and G. Landwehr, Z. Naturforsch. 21a: 495 (1966);

    ADS  Google Scholar 

  39. E. Braun and G. Landwehr, in : “Proceedings of the International Conference on the Physics of Semiconductors, Kyoto, 1966,” J. Phys. Soc. Japan Suppl. 21: 380 (1966);

    Google Scholar 

  40. E. Braun, Dissertation, Technische Hochschule Braunschweig, February 1967.

    Google Scholar 

  41. J. H. Mendum and R. N. Dexter, Bull. Am. Phys. Soc. 9: 632 (1964).

    Google Scholar 

  42. J. C. Picard and D. L. Carter, in: “Proceedings of the International Conference on the Physics of Semiconductors, Kyoto, 1966,” J. Phys. Soc. Japan Suppl. 21: 202 (1966).

    Article  Google Scholar 

  43. K. J. Button and G. Landwehr, to be published.

    Google Scholar 

  44. C. Guthmann and J.-M. Thullier, Compt. Rend. 263: 303 (1966).

    Google Scholar 

  45. J. Furdyna, Phys. Rev. Letters 16: 646 (1966).

    Article  ADS  Google Scholar 

  46. R. A. Stradling and A. Antcliffe, in: “Proceedings of the International Conference on the Physics of Semiconductors, Kyoto, 1966,” J. Phys. Soc. Japan Suppl. 21: 374 (1966).

    Google Scholar 

  47. W. Giriat, Phys. Letters 24A: 515 (1967).

    Article  ADS  Google Scholar 

  48. E. O. Kane, J. Phys. Chem. Solids 1: 249 (1957).

    Article  ADS  Google Scholar 

  49. C. S. Whitsett, Phys. Rev. 138: A829 (1965).

    Article  ADS  Google Scholar 

  50. K. F. Cuff, M. R. Ellett, and C. D. Kuglin, in: Proceedings of the International Conference on the Physics of Semiconductors, Exeter, 1962, p. 316.

    Google Scholar 

  51. K. F. Cuff, M. R. Ellett, C. D. Kuglin, and L. R. Williams, in: Proceedings of the International Conference on the Physics of Semiconductors, Paris, 1964, Dunod, Paris, 1964, p. 677.

    Google Scholar 

  52. K. Auch and G. Landwehr, Z. Naturforsch. 18a: 424 (1963).

    ADS  Google Scholar 

  53. G. Landwehr and P. Drath, in : Proceedings of the International Conference on the Physics of Semiconductors, Paris, 1964, Dunod, Paris, 1964, p. 669;

    Google Scholar 

  54. G. Landwehr and P. Drath Z. Angew. Phys. 20: 392 (1966).

    Google Scholar 

  55. J. R. Drabble, Proc. Phys. Soc. (London) 72: 380 (1958).

    Article  ADS  Google Scholar 

  56. A. Freudenhammer, Diplomarbeit T. H. Aachen, 1967.

    Google Scholar 

  57. M. H. Cohen and E. I. Blount, Phil. Mag. Vol. 115 (1960).

    Google Scholar 

  58. P. Drath and G. Landwehr, Phys. Letters 24A: 504 (1967);

    Article  ADS  Google Scholar 

  59. P. Drath and G. Landwehr,Z. Naturforsch. 23a: 1146 (1968);

    Google Scholar 

  60. P. Drath, Dissertation T. H. Braunschweig, 1967.

    Google Scholar 

  61. J. R. Burke, R. S. Allgaier, B. B. Houston, J. Babiskin, and P. G. Siebenmann, Phys. Rev. Letters 14: 360 (1965).

    Article  ADS  Google Scholar 

  62. J. R. Burke, B. Houston, H. T. Savage, J. Babiskin, and P. G. Siebenmann, in: “;Proceedings of the International Conference on the Physics of Semiconductors, Kyoto, 1966,” Phys. Soc. Japan Suppl. 21: 384 (1966).

    Google Scholar 

  63. I. Rosenmann, in : “Proceedings of the International Conference on the Physics of Semiconductors, Kyoto, 1966,” J. Phys. Soc. Japan Suppl. 21: 370 (1966).

    Google Scholar 

  64. P. N. Argyres and E. N. Adams, Phys. Rev. 104: 900 (1956).

    Article  ADS  MATH  Google Scholar 

  65. J. Appel, Z. Naturforsch. 11a: 892 (1956).

    ADS  MATH  Google Scholar 

  66. W. F. Love and W. F. Wei, Phys. Rev. 123: 67 (1961).

    Article  ADS  Google Scholar 

  67. T. J. Diesel and W. F. Love, Phys. Rev. 124: 666 (1961).

    Article  ADS  Google Scholar 

  68. S. C. Miller and M. A. Omar, Phys. Rev. 123: 74 (1961).

    Article  ADS  Google Scholar 

  69. O. Beckman, E. Hanamura and L. J. Neuringer, Phys. Rev. Letters 18: 773 (1967).

    Article  ADS  Google Scholar 

  70. E. Braun, G. Landwehr, and L. J. Neuringer, to be published.

    Google Scholar 

  71. L. S. Dubinskaya, I. I. Farbstein, and S. S. Shalyt, Zh. Eksperim. i Teor. Fiz. 54: 754 (1968).

    Google Scholar 

  72. C. Guthmann and J. M. Thullier, Proceedings of the Symposium on the Physics of Selenium and Tellurium, Montreal, 1962, in press.

    Google Scholar 

  73. L. M. Bliek and G. Landwehr, in : Proceedings of the International Conference on the Physics of Semiconductors, Moscow, 1968, in press.

    Google Scholar 

  74. L. M. Bliek and G. Landwehr, Phys. Stat. Sol. January, 1969.

    Google Scholar 

  75. L. M. Roth, S. H. Groves, and P. W. Wyatt, Phys. Rev. Letters 19: 576 (1967).

    Article  ADS  Google Scholar 

  76. G. I. Guseva and P. S. Zyryanov, Phys. Stat. Sol. 25: 775 (1968).

    Article  ADS  Google Scholar 

Download references

Author information

Author notes

  1. G. Landwehr

    Present address: Physikalisches Institut, Universität Wuerzburg, Germany

Authors and Affiliations

  1. Physikalisch-Technische Bundesanstalt, Braunschweig, Germany

    G. Landwehr

Authors
  1. G. Landwehr
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Ecole Normale Supérieure, Laboratoire de Physique and Faculté des Sciences, Université de Paris, Paris, France

    E. D. Haidemenakis

Rights and permissions

Reprints and permissions

Copyright information

© 1969 Springer Science+Business Media New York

About this chapter

Cite this chapter

Landwehr, G. (1969). The Shubnikov-de Haas Effect and Quantum-Limit Phenomena in Semiconductors. In: Haidemenakis, E.D. (eds) Physics of Solids in Intense Magnetic Fields. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-5508-1_22

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-5508-1_22

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-5510-4

  • Online ISBN: 978-1-4899-5508-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation