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.

7 pages, 4 figures; version accepted for publication in Europhys. Lett., new version contains energy calculations for collective excitations of the 4/11 state

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Cited by in corpus (12)

• Design and characterization of electronic fractals
• Quantum Hall system in Tao-Thouless limit
• Microscopic theory of the quantum Hall hierarchy
• Non-Abelian states with negative flux: a new series of quantum Hall states
• Reentrant topological phases in Mn-doped HgTe quantum wells
• Scaling flow diagram in the fractional quantum Hall regime of GaAs/AlGaAs heterostructures
• Possible Reentrance of the Fractional Quantum Hall Effect in the Lowest Landau Level
• Transition from Free to Interacting Composite Fermions away from $\nu$=1/3
• Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions
• Spin-excitations of the quantum Hall ferromagnet of composite fermions
• Magnetism, FeS colloids, and Origins of Life
• Chern-Simons theory of multi-component quantum Hall systems