Eur. Phys. J. B (2016) 89: 257
https://doi.org/10.1140/epjb/e2016-70496-4

Regular Article

The transport mechanism of the integer quantum Hall effect

¹ Department of physics, School of Physics and Telecommunication Engineering, Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, P.R. China
² School of Physics, State Key Laboratory of Optoelectronic Material and Technology, Gangdong Province Key Laboratory of Display Material and Technology, Sun Yat-Sen University, Guangzhou 510275, P.R. China

^a e-mail: wliming@scnu.edu.cn

Received: 25 August 2016
Received in final form: 24 September 2016
Published online: 28 November 2016

Abstract

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.