Fractional Quantum Hall Effect and vortex lattices.II

TL;DR

This paper shows that all observed fractional quantum Hall effect states can be explained without composite fermions, using topologically nontrivial wave functions and lattice models, revealing specific electron densities with energy gaps.

Contribution

It introduces a topological wave function approach to explain fractional quantum Hall states without composite fermions, providing new insights into electron density gaps.

Findings

All observed fractions can be derived without composite fermions.

Identifies special electron densities with energy gaps.

Calculates gaps for certain lattice models.

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. These gaps were calculated for some lattices in a simplified model.