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Mesoscopic Quantum Hall Effect pp 1–37Cite as

Introduction

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Abstract

The quantum Hall effect is one of the central subjects of the modern condensed matter physics. This effect, observed in a two-dimensional electron gas in strong magnetic fields, has several exciting features such as the precise quantization of the Hall conductance, excitations with fractional charge and fractional statistics, etc. The low energy physics of the quantum Hall effect is determined by edge excitations, because there exists a gap for excitations in the bulk of the two-dimensional gas. In this chapter we make a review of the quantum Hall physics and focus on the edge states.

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References

  1. K. v. Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45, 494 (1980)

    Google Scholar 

  2. A.M. Chang, Rev. Mod. Phys. 75, 1449 (2003)

    Google Scholar 

  3. X.-G. Wen, Adv. Phys. 44, 405 (1995)

    Article  ADS  Google Scholar 

  4. S. Datta, Electronic transport in mesoscopic systems (Cambridge University Press, Cambridge, 1999)

    Google Scholar 

  5. I. Neder, M. Heiblum, Y. Levinson, D. Mahalu, V. Umansky, Phys. Rev. Lett. 96, 016804 (2006)

    Article  ADS  Google Scholar 

  6. H. le Sueur et al., Phys. Rev. Lett. 105, 056803 (2010)

    Article  ADS  Google Scholar 

  7. C. Altimiras et al., Phys. Rev. Lett. 105, 226804 (2010)

    Article  ADS  Google Scholar 

  8. F.E. Camino, W. Zhou, V.J. Goldman, Phys. Rev. B 72, 075342 (2005)

    Article  ADS  Google Scholar 

  9. F.E. Camino, W. Zhou, V.J. Goldman, Phys. Rev. Lett. 98, 076805 (2007)

    Article  ADS  Google Scholar 

  10. F.E. Camino, W. Zhou, V.J. Goldman, Phys. Rev. B 74, 115301 (2006)

    Article  ADS  Google Scholar 

  11. R.L. Willett, L.N. Pfeiffer, K.W. West, PNAS 106, 8853 (2009)

    Article  ADS  Google Scholar 

  12. R.L. Willett, L.N. Pfeiffer, K.W. West. arXiv:0911.0345

    Google Scholar 

  13. YuV Sharvin, Sov. Phys. JETP 21, 655 (1965)

    ADS  Google Scholar 

  14. B.J. van Wees, H. van Houten, C.W.J. Beenakker, J.G. Williamson, L.P. Kouwenhoven, D. van der Marel, C.T. Foxon, Phys. Rev. Lett. 60, 848 (1988)

    Article  ADS  Google Scholar 

  15. B.J. van Wees, H. van Houten, C.W.J. Beenakker, J.G. Williamson, L.P. Kouwenhoven, D. van der Marel, C.T. Foxon, Phys. Rev. B 43, 12431 (1991)

    Article  ADS  Google Scholar 

  16. C.J. Gorter, Physica 17, 777 (1951)

    Article  ADS  Google Scholar 

  17. C.W.J. Beenakker, Phys. Rev. B 44, 1646 (1991)

    Article  ADS  Google Scholar 

  18. L.P. Gorkov, A.I. Larkin, D.E. Khmelnitskii, JETP Lett. 30, 248 (1979)

    ADS  Google Scholar 

  19. N.W. Ashcroft, N.D. Mermin, Solid State Physics (Holt, Rinehart, and Winston, New York, 1976)

    Google Scholar 

  20. V. Umansky, R. de-Picciotto, M. Heiblum, Appl. Phys. Lett. 71, 683 (1997)

    Article  ADS  Google Scholar 

  21. A. Comtet, T. Jolicoeur, S. Ouvry, F. David (eds.), Topological Aspects of Low Dimensional Systems (Springer, Berlin and Les Editions de Physique, Les Ulis, 2000)

    Google Scholar 

  22. H.P. Wei, A.M. Chang, D.C. Tsui, M. Razeghi, Phys. Rev. B 32, 7016 (1985)

    Article  ADS  Google Scholar 

  23. H.P. Wei, D.C. Tsui, A.M.M. Pruisken, Phys. Rev. B 33, 1488 (1986)

    Article  ADS  Google Scholar 

  24. Ebert G., von Klitzing K., Weimann G., J. Phys., C 18, L257 (1985)

    Google Scholar 

  25. D.C. Tsui, H.L. Stormer, A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)

    Article  ADS  Google Scholar 

  26. L. Saminadayar, D.C. Glattli, Y. Jin, B. Etienne, Phys. Rev. Lett. 79, 2526 (1997)

    Article  ADS  Google Scholar 

  27. R. de-Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin, D. Mahalu. Nature 389, 162 (1997)

    Google Scholar 

  28. R. Willett, J.P. Eisenstein, H.L. Stormer, D.C. Tsui, A.C. Gossard, J.H. English, Phys. Rev. Lett. 59, 1776 (1987)

    Article  ADS  Google Scholar 

  29. X.G. Wen, Phys. Rev. Lett. 66, 802 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. L.D. Landau, E.M. Lifshits, Theoretical Physics, vol. 3 (Butterworth-Heinemann, Oxford)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  32. D.E. Khmelnitskii, JETP Lett. 38, 552 (1983)

    ADS  Google Scholar 

  33. R.B. Laughlin, Phys. Rev. B 23, 5632 (1981)

    Article  ADS  Google Scholar 

  34. B.I. Halperin, Phys. Rev. B 25, 2185 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  35. M. Marino, Chern-Simons Theory, Matrix Models, and Topological Strings (Oxford University Press, Oxford, 2005)

    Book  MATH  Google Scholar 

  36. C. Kassel, V. Turaev, Braid Groups (Springer, Heidelberg, 2008)

    Google Scholar 

  37. E. Witten, Commun. Math. Phys. 121, 351 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. I.P. Levkivskyi, E.V. Sukhorukov, Phys. Rev. B 78, 045322 (2008)

    Article  ADS  Google Scholar 

  39. R.B. Laughlin, M.L. Cohen, J.M. Kosterlitz, H. Levine, S.B. Libby, A.M.M. Pruisken, Phys. Rev. B 32, 1311 (1985)

    Google Scholar 

  40. F.D.M. Haldane, Phys. Rev. Lett. 51, 605 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  41. R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)

    Article  ADS  Google Scholar 

  42. F.D.M. Haldane, E.H. Rezayi, Phys. Rev. B 31, 2529 (1985)

    Article  ADS  Google Scholar 

  43. R.E. Prange, S.M. Girvin, The Quantum Hall Effect (Springer, New York, 1987)

    Google Scholar 

  44. F.E. Camino, W. Zhou, V.J. Goldman, Phys. Rev. Lett. 95, 246802 (2005)

    Article  ADS  Google Scholar 

  45. Y. Ji et al., Nature (London) 422, 415 (2003)

    Article  ADS  Google Scholar 

  46. H.-S. Sim, E.V. Sukhorukov, Phys. Rev. Lett. 96, 020407 (2006)

    Article  ADS  Google Scholar 

  47. P. Samuelsson, E.V. Sukhorukov, M. Buttiker, Phys. Rev. Lett. 92, 026805 (2004)

    Article  ADS  Google Scholar 

  48. I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, V. Umansky, Nature 448, 333 (2007)

    Article  ADS  Google Scholar 

  49. P. Roulleau, F. Portier, D.C. Glattli, P. Roche, A. Cavanna, G. Faini, U. Gennser, D. Mailly, Phys. Rev. B 76, 161309 (2007)

    Article  ADS  Google Scholar 

  50. P. Roulleau, F. Portier, D.C. Glattli, P. Roche, A. Cavanna, G. Faini, U. Gennser, D. Mailly, Phys. Rev. Lett. 100, 126802 (2008)

    Article  ADS  Google Scholar 

  51. L.V. Litvin, H.-P. Tranitz, W. Wegscheider, C. Strunk, Phys. Rev. B 75, 033315 (2007)

    Article  ADS  Google Scholar 

  52. L.V. Litvin, A. Helzel, H.-P. Tranitz, W. Wegscheider, C. Strunk, Phys. Rev. B 78, 075303 (2008)

    Article  ADS  Google Scholar 

  53. E. Bieri, Correlation and interference experiments with edge states. Ph.D. thesis, University of Basel (2007)

    Google Scholar 

  54. E. Bieri, M. Weiss, O. Goktas, M. Hauser, C. Schonenberger, S. Oberholzer, Phys. Rev. B 79, 245324 (2009)

    Article  ADS  Google Scholar 

  55. M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Theoretical Physics, University of Geneva, 1211, Geneva, Switzerland

    Ivan Levkivskyi

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  1. Ivan Levkivskyi
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Correspondence to Ivan Levkivskyi .

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Levkivskyi, I. (2012). Introduction. In: Mesoscopic Quantum Hall Effect. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30499-6_1

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  • DOI: https://doi.org/10.1007/978-3-642-30499-6_1

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  • Print ISBN: 978-3-642-30498-9

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