Fractional Quantum Hall Effect and vortex lattices

TL;DR

This paper shows that the fractional quantum Hall effect can be explained through topologically nontrivial wave functions without composite fermions, revealing specific electron densities with gapped ground states.

Contribution

It introduces a topological wave function approach to explain fractional quantum Hall states, bypassing the composite fermion model.

Findings

All observed fractions explained without composite fermions

Identification of special electron densities with gapped ground states

Topological classification of many-electron wave functions

Abstract

It is demonstrated that all observed fractions at moderate Landau level fillings in 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 indicate the special values of of electron density in the ground states separated by a gap from excited energies.