The transport mechanism of the integer quantum Hall effect

TL;DR

This paper explains the integer quantum Hall effect by analyzing electron transport with semi-classical wave packets, showing how edge states prevent back scattering and produce quantized Hall resistance plateaus.

Contribution

It introduces a semi-classical wave packet model to describe electron transport and edge state separation in the quantum Hall effect, providing a new perspective on the mechanism.

Findings

Edge states prevent back scattering, leading to zero longitudinal resistance.

Landau level crossing causes electron wave overlap, resulting in resistance changes.

The model explains the quantized Hall resistance plateaus observed experimentally.

Abstract

The integer quantum Hall effect is analysed using a transport mechanism with a semi-classic wave packages of electrons in this paper. A strong magnetic field perpendicular to a slab separates the electron current into two branches with opposite wave vectors $({\it k})$ and locating at the two edges of the slab, respectively, along the current. In this case back scattering of electrons ($k\rightarrow -k$) is prohibited by the separation of electron currents. Thus the slab exhibits zero longitudinal resistance and plateaus of Hall resistance. When the Fermi level is scanning over a Landau level when the magnetic field increases, 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 plateau.