Advertisement

Journal of Experimental and Theoretical Physics

, Volume 117, Issue 3, pp 538–550 | Cite as

Anomalous hydrodynamics of fractional quantum Hall states

  • P. Wiegmann
Article

Abstract

We propose a comprehensive framework for quantum hydrodynamics of the fractional quantum Hall (FQH) states. We suggest that the electronic fluid in the FQH regime can be phenomenologically described by the quantized hydrodynamics of vortices in an incompressible rotating liquid. We demonstrate that such hydrodynamics captures all major features of FQH states, including the subtle effect of the Lorentz shear stress. We present a consistent quantization of the hydrodynamics of an incompressible fluid, providing a powerful framework to study the FQH effect and superfluids. We obtain the quantum hydrodynamics of the vortex flow by quantizing the Kirchhoff equations for vortex dynamics.

Keywords

Vortex Hall Conductance Lower Landau Level Chiral Condition Fractional Quantum Hall Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. P. Pitaevskii and E. M. Livshitz, Physical Kinetics, Course of Theoretical Physics (Butterworth-Heinemaim, 1981), vol. 10.Google Scholar
  2. 2.
    S. M. Girvin, A. H. MacDonald, and P. M. Platzman, Phys. Rev. B 33, 2481 (1986).ADSCrossRefGoogle Scholar
  3. 3.
    S. C. Zhang, T. H. Hansson, and S. A. Kivelson, Phys. Rev. Lett. 62, 82 (1989).ADSCrossRefGoogle Scholar
  4. 4.
    N. Road, Phys. Rev. Lett. 62, 86 (1989).ADSCrossRefGoogle Scholar
  5. 5.
    D.-H. Lee and S. C. Zhang, Phys. Rev. Lett. 66, 1220 (1991).ADSCrossRefGoogle Scholar
  6. 6.
    M. Stone, Phys. Rev. B 42, 212 (1990).ADSCrossRefGoogle Scholar
  7. 7.
    R. P. Feynman, Statistical Mechanics (Benjamin, Reading, Mass., 1972), ch. 11; Phys. Rev. 91, 1291, 1301 (1953); 94, 262 (1954); R. P. Feynman and M. Cohen, Ibid. 102, 1189 (1956).Google Scholar
  8. 8.
    J. E. Avion, R. Seiler, and P. G. Zograf, Phys. Rev. Lett. 75, 697 (1995).ADSCrossRefGoogle Scholar
  9. 9.
    I. V. Tokatly and G. Vignale, Phys. Rev. B 76, 161305 (2007); J. Phys. C 21, 275603 (2009).ADSCrossRefGoogle Scholar
  10. 10.
    N. Read, Phys. Rev. B 79, 045308 (2009); N. Read and E. H. Rezayi, Phys. Rev. B 84, 085316 (2011).ADSCrossRefGoogle Scholar
  11. 11.
    C. Hoyos and D. T. Son, Phys. Rev. Lett. 108, 066805 (2012).ADSCrossRefGoogle Scholar
  12. 12.
    A. G. Abanov, J. Phys. A: Math. Theor. 46, 292001 (2013).MathSciNetCrossRefGoogle Scholar
  13. 13.
    L. D. Landau, Zh. Eksp. Teor. Fiz. 11, 542 (1941); J. Phys. 5, 71; 8, 1 (1941).Google Scholar
  14. 14.
    P. Wiegmaim, arXiv:1211.5132.Google Scholar
  15. 15.
    R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).ADSCrossRefGoogle Scholar
  16. 16.
    D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982).ADSCrossRefGoogle Scholar
  17. 17.
    R. R. Du, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 70, 2944 (1993).ADSCrossRefGoogle Scholar
  18. 18.
    L. P. van Kouwenhoven, B. J. Wees, N. C. van dor Vaart, C. J. P. M. Harmans, C. E. Timmoring, and C. T. Foxon, Phys. Rev. Lett. 64, 685 (1990).ADSCrossRefGoogle Scholar
  19. 19.
    P. Wiegmaim, Phys. Rev. Lett. 108, 206810 (2012).ADSCrossRefGoogle Scholar
  20. 20.
    V. Bargmann, Rev. Mod. Phys. 34, 829 (1962).MathSciNetADSCrossRefzbMATHGoogle Scholar
  21. 21.
    V. V. Kozlov, General Theory of Vortices (Springer, 2003).zbMATHGoogle Scholar
  22. 22.
    X.-G. Wen and A. Zee, Phys. Rev. Lett. 69, 953 (1992).ADSCrossRefGoogle Scholar
  23. 23.
    I. V. Kukushkin, J. H. Smet, V. W. Scarola, V. Umansky, and K. von Klitzing, Science 324, 1044 (2009).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2013

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of ChicagoChicagoUSA

Personalised recommendations