Europhys. Lett.
Volume 68, Number 1, October 2004
Page(s) 72 - 78
Section Condensed matter: electronic structure, electrical, magnetic, and optical properties
Published online 01 September 2004
Europhys. Lett., 68 (1), pp. 72-78 (2004)
DOI: 10.1209/epl/i2004-10215-5

On the self-similarity in quantum Hall systems

M. O. Goerbig1, 2, P. Lederer2 and C. Morais Smith1

1  Département de Physique, Université de Fribourg Pérolles, CH-1700 Fribourg, Switzerland
2  Laboratoire de Physique des Solides (associé au CNRS), Bât. 510 Université Paris-Sud - F-91405 Orsay cedex, France

received 2 February 2004; accepted in final form 6 August 2004

The Hall-resistance curve of a two-dimensional electron system in the presence of a strong perpendicular magnetic field is an example of self-similarity. It reveals plateaus at low temperatures and has a fractal structure. We show that this fractal structure emerges naturally in the Hamiltonian formulation of composite fermions. After a set of transformations on the electronic model, we show that the model, which describes interacting composite fermions in a partially filled energy level, is self-similar. This mathematical property allows for the construction of a basis of higher generations of composite fermions. The collective-excitation dispersion of the recently observed 4/11 fractional-quantum-Hall state is discussed within the present formalism.

73.43.-f - Quantum Hall effects.
73.43.Cd - Theory and modeling.
71.10.Pm - Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.).

© EDP Sciences 2004