M. O. Goerbig, P. Lederer, C. Morais Smith
Published 2004-01-19, updated 2004-08-26Version 2
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.
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
Journal: Europhys. Lett. 68, 72 (2004)
Composite fermions in quantum Hall systems
Possibility of p-wave pairing of composite fermions at $ν=1/2$
Valley polarization and susceptibility of composite fermions around nu=3/2
