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

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