Composite particles in the Theory of Quantum Hall Effect

TL;DR

This paper models the formation of composite particles in the quantum Hall effect using a self-consistent field approach, explaining the observed filling factors through flux attachment and clustering phenomena.

Contribution

It introduces a model for composite particles in QHE systems based on a self-consistent field, providing a phenomenological explanation for fractional filling factors.

Findings

Ground states for primary composite particles at specific filling factors

Clustering of composite particles explains fractional quantum Hall states

Flux attachment and binding elucidate electron interactions in QHE

Abstract

The formation of composite particles in the electron liquid under QHE conditions discussed by Jain in generalizing Laughlins many-particle state is considered by using a model for two-dimensional guiding center configurations. Describing the self-consistent field of electron repulsion by a negative parabolic potential on effective centers and an inter-center amount we show that with increasing magnetic field the ground state of so-called primary composite particles $\nu=\frac{1}{q}$, $q=1,3,5,... $, is given for higher negative quantum numbers of the total angular momentum. By clustering of primary composite particles due to absorption or emission of flux quanta we explain phenomenologically the quasi-particle structure behind the series of relevant filling factors $\nu=\frac{p}{q}$, $p=1,2,3,...$. Our considerations show that the complicate interplay of electron-magnetic field and electron-electron interactions in QHE systems may be understood in terms of adding flux quanta $\Phi_0$ to charges $e$ and binding of charges by flux quanta.