Skip to main content
SpringerLink
Log in

Screening and edge states in two-dimensional metals in a magnetic field

  • Electronic Properties of Solid
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The length λ0 at which the lateral electric-field component E ⊥ perpendicular to the boundary is conserved near the boundary of two-dimensional (2D) samples, which is covered by 2D electrons, has been determined. The existence of the finite such length follows from the self-consistent process of the screening of the external fields forming the boundaries of real 2D systems by the electrons of the metal. The effect of E ⊥ on the structure of magnetic edge states has been taken into account in the mean field approximation in a wide range of the external field from the semiclassical limit (ɛF ≫ ħωc), where ɛF is the Fermi energy of the 2D system and ħωc is the cyclotron energy to the quantum Hall effect (QHE) region (ɛF ≪ ħωc). The positions of the magnetic edge state peaks against the background of their ideal distribution along the perimeter of the 2D circle in the known problem of transverse magnetic focusing have been determined in the semiclassical limit. The systematic description of the structure of the skin layer with λ H ≥ λ0, consisting of the set of the so-called integer strips (overlapping or independent), which are carriers of the universal quantum conductance, has been proposed in the QHE regime. A relatively large probability of the overlapping of the fields of adjacent strips, as well as the possibility of describing coupled integer cascades, is remarkable. The existing data on the tunneling current through integer strips in the λ H layer providing suitable information on the actual state of the boundary of the 2D system have been commented. A natural analogy between the properties of magnetic edge states and a well-known problem of the details of the ballistic conductance σ‖(H) of narrow electron channels in the magnetic field H has been noticed. The formalisms of both problems are identical under the conditions λ H ≥ w, where 2w is the effective width of the quasi-one-dimensional channel. The existing information on the σ‖(H) dependence in a wide range of the magnetic field has been systematized. The attributes of the QHE observed in σ‖(H) convincingly indicate the reality of the formation of various modifications of integer strips in inhomogeneous 2D systems in the quantizing magnetic field.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. M. Lifshitz and A. M. Kosevich, Sov. Phys. JETP 2, 646 (1955).

    Google Scholar 

  2. M. S. Khaikin, Sov. Phys. JETP 12, 152 (1960).

    Google Scholar 

  3. R. Prange and T. Nee, Phys. Rev. 168, 779 (1968).

    Article  ADS  Google Scholar 

  4. V. Tsoi, J. Bass, and P. Wyder, Rev. Mod. Phys. 71, 1641 (1999).

    Article  ADS  Google Scholar 

  5. M. Kaplit and J. Zemel, Phys. Rev. Lett. 21, 212 (1968).

    Article  ADS  Google Scholar 

  6. S. Takaoka, K. Oto, H. Kurimoto, K. Murase, K. Gamo, and S. Nishi, Phys. Rev. Lett. 72, 3080 (1994).

    Article  ADS  Google Scholar 

  7. B. Halperin, Phys. Rev. B: Condens. Matter 25, 2185 (1982).

    Article  ADS  Google Scholar 

  8. M. Büttiker, Phys. Rev. B: Condens. Matter 38, 9375 (1988); IBM J. Res. Dev. 32, 317 (1988).

    Article  ADS  Google Scholar 

  9. K. von Klitzing, Physica B (Amsterdam) 184, 1 (1993).

    Article  ADS  Google Scholar 

  10. R. Haug, Semicond. Sci. Technol. 8, 131 (1993).

    Article  ADS  Google Scholar 

  11. X. Wen, Phys. Rev. Lett. 64, 2206 (1990); Phys. Rev. B: Condens. Matter 43, 11025 (1991); Phys. Rev. B: Condens. Matter 44, 5708 (1991).

    Article  ADS  Google Scholar 

  12. C. de C. Chamon and X. G. Wen, Phys. Rev. B: Condens. Matter 49, 8227 (1994).

    Article  ADS  Google Scholar 

  13. M. Grayson, D. C. Tsui, L. N. Pfeiffer, K. W. West, and A. M. Chang, Phys. Rev. Lett. 80, 1062 (1998).

    Article  ADS  Google Scholar 

  14. M. Hilke, D. C. Tsui, M. Grayson, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 87, 186806 (2001).

    Article  ADS  Google Scholar 

  15. E. Deviatov, A. A. Kapustin, V. T. Dolgopolov, A. Lorke, D. Reuter, and A. D. Wieck, Phys. Rev. B: Condens. Matter 74, 073303 (2006).

    Article  ADS  Google Scholar 

  16. E. Andrei, Phys. Rev. Lett. 52, 1449 (1984).

    Article  ADS  Google Scholar 

  17. Yu. Monarkha, U. Albrecht, K. Kono, and P. Leiderer, Phys. Rev. B: Condens. Matter 47, 13812 (1993).

    Article  ADS  Google Scholar 

  18. P. Leiderer, S. Nazin, and V. Shikin, Low Temp. Phys. 34(4), 392 (2008).

    Article  ADS  Google Scholar 

  19. D. Chklovskii, B. Shklovskii, and L. Glazman, Phys. Rev. B: Condens. Matter 46, 4026 (1992).

    Article  ADS  Google Scholar 

  20. D. Chklovskii, K. Matveev, and B. Shklovskii, Phys. Rev. B: Condens. Matter 47, 12605 (1993).

    Article  ADS  Google Scholar 

  21. E. A. Kaner, N. M. Makarov, and I. M. Fuks, Sov. Phys. JETP 28, 483 (1968).

    ADS  Google Scholar 

  22. L. A. Fal’kovskii, Sov. Phys. JETP 31, 981 (1970).

    ADS  Google Scholar 

  23. G. B. Volovik, JETP Lett. 55, 368 (1992).

    ADS  Google Scholar 

  24. M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).

    Article  ADS  Google Scholar 

  25. I. M. Lifshitz, M. Ya. Azbel, and M. I. Kaganov, Electron Theory of Metals (Nauka, Moscow, 1971; Consultants Bureau, New York, 1973); M. Ya. Azbel’, JETP Lett. 5, 230 (1967).

    Google Scholar 

  26. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics: Part 1 (Nauka, Moscow, 1995; Butterworth-Heinemann, Oxford, 1996).

    Google Scholar 

  27. K. Berggren and D. Newson, Semicond. Sci. Technol. 1, 327 (1986).

    Article  ADS  Google Scholar 

  28. T. Demel, D. Heitman, P. Grambow, and K. Ploog, Phys. Rev. B: Condens. Matter 38, 12732 (1998).

    Article  ADS  Google Scholar 

  29. S. Laux, D. Frank, and F. Stern, Surf. Sci. 196, 101 (1988).

    Article  ADS  Google Scholar 

  30. V. B. Shikin, Sov. Phys. JETP 74, 852 (1991).

    Google Scholar 

  31. J. Eisenstein, L. Pfeifer, and K. West, Phys. Rev. B: Condens. Matter 50, 1760 (1994).

    Article  ADS  Google Scholar 

  32. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Nauka, Moscow, 1982; Butterworth-Heinemann, Oxford, 1984).

    Google Scholar 

  33. W. Dietsche, K. von Klitzing, K. Ploog, and K. Eberl, Semicond. Sci. Technol. 10, 117 (1995); W. Dietsche, K. von Klitzing, and K. Ploog, Surf. Sci. 361, 117 (1996).

    Article  ADS  Google Scholar 

  34. V. Shikin, Phys. Rev. B: Condens. Matter 64, 245335 (2001).

    Article  ADS  Google Scholar 

  35. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 2: The Classical Theory of Fields (Nauka, Moscow, 1973; Butterworth-Heinemann, Oxford, 1980).

    Google Scholar 

  36. V. Fock, Z. Phys. 47, 446 (1928).

    Article  ADS  Google Scholar 

  37. K. Berggren, T. Thornton, D. Newson, and M. Pepper, Phys. Rev. Lett. 57, 1769 (1986).

    Article  ADS  Google Scholar 

  38. T. Thornton, M. Pepper, H. Ahmed, D. Andrews, and G. J. Davies, Phys. Rev. Lett. 56, 1198 (1986).

    Article  ADS  Google Scholar 

  39. 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: Condens. Matter 38, 3625 (1988).

    Article  ADS  Google Scholar 

  40. H. Linke, L. Christensson, P. Omling, and P. E. Lindelof, Phys. Rev. B: Condens. Matter 56, 1440 (1997).

    Article  ADS  Google Scholar 

  41. P. Boggild, A. Kristensen, H. Bruus, S. M. Reimann, and P. E. Lindelof, Phys. Rev. B: Condens. Matter 57, 15408 (1998).

    Article  ADS  Google Scholar 

  42. M. Yu. Mel’nikov, V. T. Dolgopolov, V. S. Khrapai, and D. Shukh, JETP Lett. 88, 36 (2008).

    Article  ADS  Google Scholar 

  43. S. Iordansky, Solid State Commun. 43, 1 (1982).

    Article  ADS  Google Scholar 

  44. A. MacDonald, T. Rice, and W. Brinkman, Phys. Rev. B: Condens. Matter 28, 3648 (1983).

    Article  ADS  Google Scholar 

  45. I. V. Kukushkin, S. V. Meshkov, and V. B. Timofeev, Sov. Phys. Usp. 31, 511 (1988).

    Article  ADS  Google Scholar 

  46. M. Fogler, Phys. Rev. B: Condens. Matter 69, 245321 (2004).

    Article  ADS  Google Scholar 

  47. V. B. Shikin, JETP Lett. 84, 27 (2006).

    Article  Google Scholar 

  48. I. Larkin and V. Shikin, Phys. Lett. A 151, 1406 (1990).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432, Russia

    V. B. Shikin & S. S. Nazin

Authors
  1. V. B. Shikin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. S. Nazin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. B. Shikin.

Additional information

Original Russian Text © V.B. Shikin, S.S. Nazin, 2011, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2011, Vol. 140, No. 2, pp. 350–367.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shikin, V.B., Nazin, S.S. Screening and edge states in two-dimensional metals in a magnetic field. J. Exp. Theor. Phys. 113, 306–321 (2011). https://doi.org/10.1134/S1063776111060203

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776111060203

Keywords

Search

Navigation