Composite-particles (Boson, Fermion) Theory of Fractional Quantum Hall Effect

TL;DR

This paper develops a quantum statistical theory for the fractional quantum Hall effect using composite particles with fluxons, explaining quantized Hall conductance without relying on Laughlin's theory.

Contribution

It introduces a new composite-particle framework with fluxons to explain fractional quantum Hall states, differing from traditional Laughlin-based models.

Findings

Predicts quantized Hall conductivity at ^2/h for illing factors /m.

Connects composite particle densities with electron and boson densities.

Provides a fluxon-based explanation for fractional charges and conductance values.

Abstract

A quantum statistical theory is developed for a fractional quantum Hall effects in terms of composite bosons (fermions) each of which contains a conduction electron and an odd (even) number of fluxons. The cause of the QHE is by assumption the phonon exchange attraction between the conduction electron ("electron", "hole") and fluxons (quanta of magnetic fluxes). We postulate that c-fermions with \emph{any} even number of fluxons have an effective charge (magnitude) equal to the electron charge $e$. The density of c-fermions with $m$ fluxons, $n_\phi^{(m)}$, is connected with the electron density $n_{\mathrm e}$ by $n_\phi^{(m)}=n_{\mathrm e}/m$, which implies a more difficult formation for higher $m$, generating correct values $me^2/h$ for the Hall conductivity $\sigma_{\mathrm H}\equiv j/E_{\mathrm H}$. For condensed c-bosons the density of c-bosons-with-$m$ fluxons, $n_\phi^{(m)}$, is connected with the boson density $n_0$ by $n_\phi^{(m)}=n_0/m$. This yields $\sigma_{\mathrm H}=m\,e^2/h$ for the magnetoconductivity, the value observed of the QHE at filling factor $\nu=1/m$ ($m=$odd numbers). Laughlin's theory and results about the fractional charge are not borrowed in the present work.