On the self-similarity in quantum Hall systems

TL;DR

This paper demonstrates that the fractal self-similarity observed in quantum Hall systems naturally emerges in the Hamiltonian framework of composite fermions, enabling the construction of higher-generation states and explaining experimental phenomena.

Contribution

It introduces a Hamiltonian-based model showing self-similarity in composite fermions, facilitating the understanding of complex fractional quantum Hall states.

Findings

Fractal structure emerges in the Hamiltonian formulation of composite fermions.

Self-similarity allows for constructing higher-generation composite fermion states.

Explains the dispersion of the 4/11 fractional quantum Hall state.

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.