A novel model for the fractional quantum Hall effect

TL;DR

This paper introduces a new quantum harmonic oscillator model that explains the fractional quantum Hall effect, including observed conductivity sequences and related physical quantities, with analytical expressions for resistance and voltage.

Contribution

It presents a novel complex quantum harmonic oscillator model that accounts for FQHE phenomena and provides analytical formulas for related physical parameters.

Findings

Explains FQHE conductivity and charge sequences.

Derives analytical expressions for resistance and voltage.

Identifies degeneracy states with specific angular momenta.

Abstract

A novel model of complex quantum harmonic oscillator is found to account for the observed Fractional quantum Hall effect (FQHE). The sequences of the observed FQHE conductivity and charge are explained. The two sequences are found to express a quantity and its complex conjugated partner. The oscillator is found to have two degenerates states, $\psi_n$, with angular momenta $\pm \,n\,\hbar$\,, where $h = 2\pi \hbar $ is the Planck's constant, and $n$ is the principal quantum number of the oscillator. The filling factor, $i$, that Klitzing has found for the integer quantum Hall effect (IQHE) is $i=n+1$. Analytical expressions for longitudinal resistance and Hall's voltage are obtained. The width of the plateau between two states is found to be $\Delta B=\frac{1}{n(n+1)}\,\frac{n_sh}{e}\,,$ where $n_s$ is the electron number density.