Fractional Quantum Hall Effect and vortex lattices

TL;DR

This paper shows that the observed fractional quantum Hall effect fractions can be explained without composite fermions, using topologically nontrivial wave functions and their classification.

Contribution

It introduces a wave function approach based on topological properties, avoiding the composite fermion concept for explaining fractional quantum Hall states.

Findings

All observed fractions can be derived without composite fermions.

Topologically nontrivial wave functions correspond to specific electron densities.

Ground states are separated by a gap from excited states.

Abstract

It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special topologically nontrivial many-electron wave functions is considered. Their group classification indicates the special values of of electron density in the ground states separated by a gap from excited states.