2004/01/31 by M. O. Goerbig, P. Lederer, C. Morais Smith
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1209/epl/i2004-10215-5
published as Europhys. Lett. 68, 72 (2004) · 7 pages, 4 figures; version accepted for publication in Europhys. Lett., new version contains energy calculations for collective excitations of the 4/11 state
arxiv created 2004/08/26 · arxiv updated 2009/12/01
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.