A study of the fractional quantum Hall effect: Odd and even denominator plateaux

TL;DR

This paper proposes a novel approach to the fractional quantum Hall effect by analyzing how changes in Hamiltonian symmetry due to magnetic field and impurities lead to both odd and even denominator plateaux, unifying it with the integer quantum Hall effect.

Contribution

It introduces a new model linking symmetry breaking in the Hamiltonian to the emergence of fractional quantum Hall plateaux, including even denominators, unifying it with the integer quantum Hall effect.

Findings

Explains the occurrence of odd and even denominator plateaux.

Provides a physical rationale for the predominance of odd denominators.

Unifies the fractional and integer quantum Hall effects under a common framework.

Abstract

We present a different approach to the fractional quantum Hall effect (FQHE), focusing it as a consequence of the change in the symmetry of the Hamiltonian of every electron in a two-dimensional electron gas (2DEG) under the application of a magnetic field and in the presence of an electrostatic potential due to the ionized impurities, and leading to a breaking of the degeneration of the Landau levels. As the magnetic field increases the effect of that electrostatic potential evolves, changing in turn the spatial symmetry of the Hamiltonian: from continuous to discrete one. The aim of both works is to give a different picture not only of the FQHE phenomenon, but a coherent one with the integer quantum Hall effect (IQHE) and consistent with the model already described in Hidalgo7, 8, 9. Therefore the model gives a global view of both effects, showing that they are aspects of the same phenomenon, and justifying not only the appearance of the odd denominator plateaux but also the even ones; and giving some physical reasons for the experimental fact that there are much more odd than even denominator plateaux, hardly observed