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Theories of the Fractional Quantum Hall Effect

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High Magnetic Fields

Part of the book series: Lecture Notes in Physics ((LNP,volume 595))

Abstract

This is an introduction to the microscopic theories of the FQHE. After a brief description of experiments, trial wavefunctions and the physics they contain are discussed. This is followed by a description of the hamiltonian approach, wherein one goes from the electrons to the composite fermions by a series of transformations. The theory is then compared to other theoretical approaches and to experiment.

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References

  1. For a review see The Quantum Hall Effect, Edited by R.E. Prange and S.M Girvin, Springer-Verlag, 1990, T. Chakraborty and P. Pietiäïnen, The Fractional Quantum Hall Effect: Properties of an incompressible quantum fluid, Springer Series in Solid State Sciences, 85, Springer-Verlag New York, 1988, A.H. MacDonald ed., Quantum Hall Effect: A Perspective, Kluwer, Boston, 1989. A. Karlhede, S. A. Kivelson and S. L. Sondhi, “The Quantum Hall Effect: The Article”, in V.J. Emery ed., “Correlated Electron Systems”, World Scientific, Singapore (1993)

    Google Scholar 

  2. Perspectives in Quantum Hall Effects, Edited by Sankar Das Sarma and Aron Pinczuk (Wiley, New York, 1997).

    Google Scholar 

  3. Composite Fermions, Edited by Olle Heinonen, World Scientific, Singapore, (1998).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  5. D. Tsui, H. Stromer and A. Gossard, Phys. Rev. Lett., 48, 1599, (1982). (FQHE).

    ADS  Google Scholar 

  6. R. B. Laughlin, Phys. Rev. Lett, 50, 1395, (1983). Needs no explanation.

    Article  ADS  Google Scholar 

  7. J. Jain, Phys. Rev. Lett., 63, 199, (1989). For the latest summary see J.K. Jain and R. Kamilla, in Ref( 8).

    Article  ADS  Google Scholar 

  8. S.M. Girvin, A.H. MacDonald and P. Platzman, Phys. Rev. B33, 2481, (1986).

    ADS  Google Scholar 

  9. B.I. Halperin, Helv. Phys. Acta 56, 75, (1983). B.I. Halperin, Phys. Rev. Lett., 52, 1583, (1984).

    Google Scholar 

  10. J.M. Leinaas and J. Myrheim, Nuovo Cimento 37B, 1 (1977). F. Wilczek, Phys. Rev. Lett. 48, 1144, (1982).

    ADS  Google Scholar 

  11. R. L. Laughlin, Phys. Rev. Lett., 60, 2677, (1988). See also A.L.Fetter, C.B. Hanna, and R.B. Laughlin, Phys. Rev. B39, 9679, (1989), ibid 43, 309, (1991).

    Article  ADS  Google Scholar 

  12. N. Read Semi. Cond. Sci. Tech., 9, 1859, (1994), and Surface Science, 361/362, 7, (1995).

    Article  ADS  Google Scholar 

  13. E. Rezayi and N. Read, Phys. Rev. Lett,72, 900, (1994).

    Article  ADS  Google Scholar 

  14. A. Stern, and B.I. Halperin, Phys. Rev. B54, 11114 (1996). See the review on modifications of RPA by S.Simon, J. Phys. Cond. Mat., 48, 10127 (1996).

    ADS  Google Scholar 

  15. S. Deser, R. Jackiw and S. Templeton, Phys. Lett., B139, 371, Field theories in condensed matter physics, E. Fradkin, Addison-Wesley, Reading MA 1991.

    Google Scholar 

  16. A. Lopez and E. Fradkin, Phys. Rev. B 44, 5246, (1991), ibid 47, 7080, (1993), Phys. Rev. Lett., 69, 2126, (1992).

    ADS  Google Scholar 

  17. R. Rajaraman and S. L. Sondhi, Mod. Phys. Lett. B 8, 1065 (1994).

    Article  ADS  Google Scholar 

  18. V. Kalmeyer and S. C. Zhang, Phys. Rev. B46, 9889, (1992).

    ADS  Google Scholar 

  19. B. I. Halperin, P.A. Lee and N. Read, Phys. Rev. B47, 7312, (1993).

    ADS  Google Scholar 

  20. W. Kang, H.L. Störmer, L.N. Pfeiffer, K.W. Baldwin and K.W. West, Phys. Rev. Lett., 71, 3850, (1993).

    Article  ADS  Google Scholar 

  21. V.J. Goldman, B. Su and J. K. Jain, Phys. Rev. Lett., 72, 2065, (1994).

    Article  ADS  Google Scholar 

  22. J.H. Smet, D. Weiss, R.H. Blick, G. Lutjering and K. von Klizting, Phys. Rev. Lett., 77, 2272, (1996).

    Article  ADS  Google Scholar 

  23. R.L. Willett, M.A. Paalanen, R.R. Ruel, K.W. West, L.N. Pfeiffer, and D.J. Bishop, Phys. Rev. Lett. 54, 112 (1990) For a review see R. Willett, Advances in Physics., 46, 447, (1997).

    Article  ADS  Google Scholar 

  24. Y.B. Kim, A. Furusaki and P.A. Lee, Phys. Rev. B50, 17917, (1994).

    ADS  Google Scholar 

  25. S.C. Zhang, H. Hansson and S. Kivelson, Phys. Rev. Lett., 62, 82, (1989). See also D.-H. Lee and S.-C. Zhang, Phys. Rev. Lett. 66, 1220 (1991), S.C. Zhang, Int. J. Mod. Phys., B6, 25, (1992) and C. L. Kane, S. Kivelson, D.H. Lee and S.C.Zhang, Phys. Rev. B 43, 3255 (1991).

    Article  ADS  Google Scholar 

  26. S.M. Girvin and A.H. MacDonald, Phys. Rev. Lett. 58, 1252, (1987). See also S. M. Girvin in Ref. 8 for work pointing to Chern-Simons theories.

    Article  ADS  Google Scholar 

  27. N. Read, Phys. Rev. Lett. 62, 86, (1989).

    Article  ADS  Google Scholar 

  28. R. Shankar and G. Murthy, Phys. Rev. Lett., 79, 4437, (1997). For details see “Field Theory of the FQHE”, in Heinonen’s book (Ref. ( 8) or cond-mat 9802244.

    Article  ADS  Google Scholar 

  29. D. Bohmand D. Pines, Phys. Rev. 92, 609, (1953).

    Article  ADS  MathSciNet  Google Scholar 

  30. G. Murthy and R. Shankar, Phys. Rev. B 59, 12260, (1999), G.Murthy, R.Shankar, K.Park, and J.K.Jain, Phys. Rev. B58, 13263, (1998).

    ADS  Google Scholar 

  31. R. Shankar, Phys. Rev. Lett., 83, 2382, (1999) cond-mat 9903064.

    Article  ADS  Google Scholar 

  32. V. Pasquier and F.D.M. Haldane Nucl. Phys. 516, 719, (1998).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  33. N. Read, Phys. Rev. B58, 16262, (1998).

    ADS  Google Scholar 

  34. G. Murthy, cond mat. 9903187.

    Google Scholar 

  35. B.I. Halperin and A. Stern, Phys. Rev. Lett., 80, 5457 (1998); G. Murthy and R.Shankar, ibid, 5458 (1998). A. Stern, B.I. Halperin, F. von Oppen and S.Simon, Phys. Rev., 59,12547, (1999). cond-mat 9812135.

    Article  ADS  Google Scholar 

  36. D.H. Lee, Phys. Rev. Lett., 80, 4745 (1998).

    Article  ADS  Google Scholar 

  37. F.C. Zhang and S. Das Sarma, Phys. Rev. B 33, 2908, (1986).

    ADS  Google Scholar 

  38. K. Park, N. Meskini, and J.K. Jain, J. Phys. Condensed Matter, 11, 7283, (1999). Has a response to R.Morf, Phys. Rev. Lett. 83, 1485, (1999).

    Article  ADS  Google Scholar 

  39. R.H. Morf, N. d’Ambrumenil and S. Das Sarma (to be published).

    Google Scholar 

  40. R.R. Du, A.S. Yeh, H.L. Störmer, D.C. Tsui, L. N. Pfeiffer, K.W. Baldwin and K.W. West, Phys. Rev. Lett., 70, 2944, (1993).

    Article  ADS  Google Scholar 

  41. W. Pan, H.L. Störmer, D.C. Tsui, L.N. Pfeiffer, K.W. Baldwin and K.W. West, Phys. Rev., B61, R5101, (2000).

    ADS  Google Scholar 

  42. R. Shankar, Phys. Rev. Lett., 84, 3946, (2000) cond-mat 9911288.

    Article  ADS  Google Scholar 

  43. R. Shankar, Phys. Rev B 63, 085322, (2001), cond-mat 0009361.

    ADS  Google Scholar 

  44. I.V. Kukushkin, K. v. Klitzing and K. Eberl, Phys. Rev. Lett. 82, 3665, (1999.)

    Article  ADS  Google Scholar 

  45. A.E. Dementyev, N.N. Kuzma, P. Khandelwal, S.E. Barrett, L.N. Pfeiffer, and K. W. West, Phys. Rev. Lett., 83, 5074, (1999). cond-mat/9907280.

    Article  ADS  Google Scholar 

  46. S. Melinte, N. Freytag, M. Horvatic, C. Berthier, L.P. Levy, V. Bayot and M. Shayegan, Phys. Rev. Lett., 84, 354, (2000). cond-mat/9908098 are the source of P(θ = 0). The rest are from N. Freytag, L. Levy, M. Horvatic, C. Berthier, and M. Shayegan, unpublished.

    Article  ADS  Google Scholar 

  47. For a recent review see A.G. Rojo, Electron-drag effects in coupled electron systems J. Phys. Cond. Mat., 11(5): R31–R52, (1999). For some very early work see G.L. Zheng and A.H. Macdonald, Phys. Rev B 48, 8203, (1993). For work on FQHE see for example I. Ussishkin I and A. Stern Phys. rev., 56 (7), 4013, (1997).

    Article  ADS  MathSciNet  Google Scholar 

  48. For a review see S. M. Girvin, ‘The Quantum Hall Effect: Novel Excitations and Broken Symmetries,’ 120 pp. Les Houches Lecture Notes, in Topological Aspects of Low Dimensional Systems, ed. by Alain Comtet, Thierry Jolicoeur, Stephane Ouvry and Francois David, (Springer-Verlag, Berlin and Les Editions de Physique, Les Ulis, 2000, ISBN: 3-540-66909-4). cond-mat/9907002, The first papers were S. L. Sondhi, A. Karlhede, S. A. Kivelson, E. H. Rezayi, Phys. Rev. B 47, 16419 (1993). H.A. Fertig, L. Brey, R. Côté, A.H. MacDonald, A. Karlhede, and S.L. Sondhi, Phys. Rev. B 55, 10671 (1997), and S. E. Barrett et al., Phys. Rev. Lett., 74, 5112 (1995).

    Google Scholar 

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Authors and Affiliations

  1. Yale University, New Haven, CT, 06520, USA

    R. Shankar

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  1. R. Shankar
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Editors and Affiliations

  1. Grenoble High Magnetic Field Laboratory, BP 166, 38042, Grenoble Cedex 9, France

    C. Berthier , L. P. Lévy  & G. Martinez ,  & 

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Shankar, R. (2002). Theories of the Fractional Quantum Hall Effect. In: Berthier, C., Lévy, L.P., Martinez, G. (eds) High Magnetic Fields. Lecture Notes in Physics, vol 595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45649-X_2

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  • DOI: https://doi.org/10.1007/3-540-45649-X_2

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  • Print ISBN: 978-3-540-43979-0

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