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Spectroscopy of Quantum Hall Edge States at Complex Filling Factors

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Mesoscopic Quantum Hall Effect

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

We propose direct experimental tests of the effective models of fractional quantum Hall edge states. We first illustrate the effective models classification with the example of a quantum Hall fluid at filling factor 2/3. We show that, in this example, it is impossible to describe the edge states with only one chiral channel and that there are several inequivalent models of the edge states with two fields. We focus our attention on the four simplest models of the edge states of a fluid with filling factor 2/3 and evaluate charges and scaling dimensions of quasi-particles. We study transport through an electronic Fabry-Perot interferometer and show that scaling properties of the Fourier components of Aharonov-Bohm oscillations in the current provide information about the electric charges and scaling dimensions of quasi-particles. Thus, such interferometers can be used to discriminate between different effective models of fluids corresponding to the same filling factor.

Some text sections in this chapter are reproduced from Phys. Rev. B 80, 045319 (2009), © American Physical Society.

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Notes

  1. 1.

    Numerical simulations [37] show that for larger values of statistical phases the quantum Hall state is not stable, and electrons form a Wigner crystal [5].

  2. 2.

    We assume that both quantum point contacts are either in a weak tunneling regime or in a weak backscattering regime.Moreover, we further assume that two channels at each quantum Hall edge originate from the same Ohmic contact, and therefore, they are equally biased.

References

  1. G. ’t Hooft, Proceedings of the Salamfest, 0284–0296 (1993)

    Google Scholar 

  2. L. Susskind, J. Math. Phys. 36, 6377 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998)

    Google Scholar 

  4. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri, Y. Oz, Phys. Rep. 323, 183 (2000)

    Article  MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

  6. X.-G. Wen, Phys. Rev. B 41, 12838 (1990)

    Article  ADS  Google Scholar 

  7. J. Fröhlich, A. Zee, Nucl. Phys. B 364, 517 (1991)

    Article  ADS  Google Scholar 

  8. J. Fröhlich, T. Kerler, Nucl. Phys. B 354, 369 (1991)

    Article  ADS  Google Scholar 

  9. J. Fröhlich, B. Pedrini, C. Schweigert, J. Walcher, J. Stat. Phys. 103, 527 (2001)

    Article  MATH  Google Scholar 

  10. J. Fröhlich, U.M. Studer, E. Thiran, J. Stat. Phys. 86, 821 (1997)

    Article  ADS  MATH  Google Scholar 

  11. X.-G. Wen, Phys. Rev. B 44, 5708 (1991)

    Article  ADS  Google Scholar 

  12. A.M. Chang, L.N. Pfeiffer, K.W. West, Phys. Rev. Lett. 77, 2538 (1996)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. For a review, see A.M. Chang, Rev. Mod. Phys. 75, 1449 (2003)

    Google Scholar 

  15. D.B. Chklovskii, B.I. Shklovskii, L.I. Glazman, Phys. Rev. B 46, 4026 (1992)

    Article  ADS  Google Scholar 

  16. C.L. Kane, M.P. Fisher, J. Polchinski, Phys. Rev. Lett. 72, 4129 (1994)

    Article  ADS  Google Scholar 

  17. C.L. Kane, M.P.A. Fisher, Phys. Rev. B 51, 13449 (1995)

    Google Scholar 

  18. S. Khlebnikov, Phys. Rev. B 73, 045331 (2006)

    Article  ADS  Google Scholar 

  19. C.L. Kane, M.P.A. Fisher, Phys. Rev. Lett. 72, 724 (1994)

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

  22. M. Dolev, M. Heiblum, V. Umansky, A. Stern, D. Mahalu, Nature 452, 829 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

  25. V.V. Ponomarenko, D.V. Averin, Phys. Rev. Lett. 99, 066803 (2007)

    Article  ADS  Google Scholar 

  26. R. Guyon, P. Devillard, T. Martin, I. Safi, Phys. Rev. B 65, 153304 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  30. I. Neder, F. Marquardt, M. Heiblum, D. Mahalu, V. Umansky, Nat. Phys. 3, 534 (2007)

    Article  Google Scholar 

  31. E.V. Sukhorukov, V.V. Cheianov, Phys. Rev. Lett. 99, 156801 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. J.T. Chalker, Y. Gefen, M.Y. Veillette, Phys. Rev. B 76, 085320 (2007)

    Article  ADS  Google Scholar 

  34. I. Neder, E. Ginossar, Phys. Rev. Lett. 100, 196806 (2008)

    Article  ADS  Google Scholar 

  35. S.-C. Youn, H.-W. Lee, H.-S. Sim, Phys. Rev. Lett. 100, 196807 (2008)

    Article  ADS  Google Scholar 

  36. I.P. Levkivskyi, E.V. Sukhorukov, Phys. Rev. Lett. 103, 036801 (2009)

    Article  ADS  Google Scholar 

  37. X. Zhu, S.G. Louie, Phys. Rev. B 52, 5863 (1995)

    Google Scholar 

  38. I.P. Levkivskyi, A. Boyarsky, J. Fröhlich, E.V. Sukhorukov, Phys. Rev. B 80, 045319 (2009)

    Article  ADS  Google Scholar 

  39. X.G. Wen, Phys. Rev. Lett. 64, 2206 (1990)

    Article  ADS  Google Scholar 

  40. A.H. MacDonald, Phys. Rev. Lett. 64, 220 (1990)

    Article  ADS  Google Scholar 

  41. M.D. Johnson, A.H. MacDonald, Phys. Rev. Lett. 67, 2060 (1991)

    Article  ADS  Google Scholar 

  42. J.K. Jain, Phys. Rev. Lett. 63, 199 (1989)

    Article  ADS  Google Scholar 

  43. Z.-X. Hu, H. Chen, K. Yang, E.H. Rezayi, X. Wan, Phys. Rev. B 78, 235315 (2008)

    Article  ADS  Google Scholar 

  44. R.G. Clark, S.R. Haynes, J.V. Branch, A.M. Suckling, P.A. Wright, P.M.W. Oswald, J.J. Harris, C.T. Foxon, Surf. Sci. 229, 25 (1990)

    Article  ADS  Google Scholar 

  45. J.P. Eisenstein, H.L. Stormer, L.N. Pfeiffer, K.W. West, Phys. Rev. B 41, 7910 (1990)

    Article  ADS  Google Scholar 

  46. L.W. Engel, S.W. Hwang, T. Sajoto, D.C. Tsui, M. Shayegan, Phys. Rev. B 45, 3418 (1992)

    Article  ADS  Google Scholar 

  47. 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 

  48. 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 

  49. E. Bieri, Correlation and interference experiments with edge states, Ph.D. Thesis, University of Basel, 2007

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

  56. J.A. Simmons, H.P. Wei, L.W. Engel, D.C. Tsui, M. Shayegan, Phys. Rev. Lett. 63, 1731 (1989)

    Article  ADS  Google Scholar 

  57. J.A. Simmons, S.W. Hwang, D.C. Tsui, H.P. Wei, L.W. Engel, M. Shayegan, Phys. Rev. B 44, 12933 (1991)

    Article  ADS  Google Scholar 

  58. B. Rosenow, B.I. Halperin, Phys. Rev. Lett. 98, 106801 (2007)

    Article  ADS  Google Scholar 

  59. B.I. Halperin, A. Stern, I. Neder, B. Rosenow, Phys. Rev B 83, 155440 (2011)

    Article  ADS  Google Scholar 

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  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). Spectroscopy of Quantum Hall Edge States at Complex Filling Factors. In: Mesoscopic Quantum Hall Effect. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30499-6_7

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  • DOI: https://doi.org/10.1007/978-3-642-30499-6_7

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