A novel model for the fractional quantum Hall effect

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.