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|
On the self-similarity in quantum Hall systems
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
Accepted: 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.
PACS: 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
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