The transport mechanism of the integer quantum Hall effect

  • Tan Hui
  • W. LiMingEmail author
  • Shi-Dong Liang
Regular Article


The integer quantum Hall effect (IQHE) is analysed using a mechanism of the electron transport in the form of semi-classic wave packages in this paper. Due to the confinement of the edges of a slab the Landau levels of electrons in a strong magnetic field go up at large wave-vectors to form energy bands. The slopes of the energy bands give the group velocities of electron wave packages and thus contribute to the current. Certain magnetic fields separate the electron transport in the slab into two branches with opposite and large wave vectors, which are localized at the two edges of the slab, respectively. In this case back scattering of electrons is prohibited due to the localization of these two branches. Thus the slab exhibits zero longitudinal resistance and plateaus of Hall resistance. When the Fermi level is sweeping over a Landau level at some magnetic fields, however, the electron waves locate around the central axis of the slab and overlap each other thus back scattering of electrons takes place frequently. Then longitudinal resistance appears and the Hall resistance goes up from one plateau to a new one. This transport mechanism is much clearer and more intuitive than the conventional explanations to the IQHE.


Solid State and Materials 


  1. 1.
    K. von Klitzing et al., Phys. Rev. Lett. 45, 494 (1980)ADSCrossRefGoogle Scholar
  2. 2.
    D.C. Tsui et al., Phys. Rev. Lett. 48, 1559 (1982)ADSCrossRefGoogle Scholar
  3. 3.
    C.-Z. Chang et al., Science 340, 167 (2013)ADSCrossRefGoogle Scholar
  4. 4.
    R.E. Prange, Phys. Rev. B 23, 5632 (1981)CrossRefGoogle Scholar
  5. 5.
    R.E. Prange, The Quantum Hall Effect, 2nd edn. (Springer-Verlag, 1990)Google Scholar
  6. 6.
    Z.F. Ezawa, in Quantum Hall Effects: Field Theoretical Approach and Related Topics, 2nd edn. (Peking University Press, 2012), p. 182Google Scholar
  7. 7.
    Ni Guangjiong, Chen Suqing, in Advanced Quantum Mechanics (in Chinese) (Fudan University Press, 2000), p. 310Google Scholar
  8. 8.
    D.J. Thouless, M. Kohmoto, P. Nightingale, M. den Nijs, Phys. Rev. Lett. 49, 405 (1982)ADSCrossRefGoogle Scholar
  9. 9.
    Q. Niu, D.J. Thouless, Y.-S. Wu, Phys. Rev. B 31, 3372 (1985)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Yasuhiro Hatsugai, Phys. Rev. B 48, 11851 (1993)ADSCrossRefGoogle Scholar
  11. 11.
    S. Datta, in Electronic Transport in Mesoscopic systems (Cambridge University Press, 1995), p. 181Google Scholar
  12. 12.
    Yan Shou Sheng, in Basis on solid state physics (in Chinese) (Peking University, 2003), p. 126Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of physicsSchool of Physics and Telecommunication Engineering, Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal UniversityGuangzhouP.R. China
  2. 2.School of Physics, State Key Laboratory of Optoelectronic Material and Technology, Gangdong Province Key Laboratory of Display Material and Technology, Sun Yat-Sen UniversityGuangzhouP.R. China

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