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On the self-similarity in quantum Hall systems

M. O. Goerbig·P. Lederer·C. Morais Smith
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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.

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M. O. Goerbig, P. Lederer, C. Morais Smith. 2004-08-26. On the self-similarity in quantum Hall systems. https://doi.org/10.1209/epl%2Fi2004-10215-5

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