On the self-similarity in quantum Hall systems
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0401340,
title = {On the self-similarity in quantum Hall systems},
author = {M. O. Goerbig and P. Lederer and C. Morais Smith},
journal= {arXiv preprint arXiv:cond-mat/0401340},
year = {2007}
}
Comments
7 pages, 4 figures; version accepted for publication in Europhys. Lett., new version contains energy calculations for collective excitations of the 4/11 state