R. Keiper | Searcharxiv

arXiv1998

Composite particles in the Theory of Quantum Hall Effect

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 $ν=\frac{1}{q}$, $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 $ν=\frac{p}{q}$, $p=1,2,3,...$. 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 $Φ_0$ to charges $e$ and binding of charges by flux quanta.

cond-mat.mes-hall↗

arXiv1995

Topological Investigation of the Fractionally Quantized Hall Conductivity

Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions under FQHE conditions are treated as functional connections over the torus, the torus being the underlying two-dimensional manifold. Relations to the $(2+1)$--dimensional Chern--Simons theory are indicated. The conductivity being a topological invariant is given as $\frac{e^2}{h}$ times a linking number which is the quotient of the winding numbers of the self-consistent field and the magnetic field, respectively. Odd denominators are explained by the two spin structures which have been considered for the FQHE correlated electron system.

cond-mat↗