Non interacting electron gas model of quantum Hall effect

TL;DR

This paper presents a non-interacting electron gas model that explains both integer and fractional quantum Hall effects without invoking fractional charge quasi-particles, suggesting a similarity to superconductivity.

Contribution

It introduces a simplified non-interacting electron gas model that unifies the explanation of quantum Hall effects, contrasting with Laughlin's interaction-based approach.

Findings

Model explains integer and fractional quantum Hall effects quickly and unified

Shows quantum Hall effect shares physical nature with superconductivity

Avoids need for fractional charge quasi-particles and fractional statistics

Abstract

On the basis of our previous studies on energy levels and wave functions of single electrons in a strong magnetic field, the energy levels and wave functions of non-interacting electron gas system, electron gas Hall surface density and Hall resistance of electron gas system are calculated. Then, a comparison is made between non-interaction electron gas model and Laughlin's interaction two dimensional electron gas system. It is found that the former can more quickly and unified the explain the integer and the fractional quantum Hall effects without the help of concepts proposed by Laughlin, such as fractionally charged quasi-particles and quasi-holes which obey fractional statistics. After explicit calculation, it is also discovered that quantum Hall effect has the same physical nature as superconducting state.