Modular Groups, Visibility Diagram and Quantum Hall Effect

Details Modular Groups, Visibility Diagram and Quantum Hall Effect Modular Groups, Visibility Diagram and Quantum Hall Effect

1997-01-30

arxiv.org/abs/cond-mat/9701219v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

17 pages, plain TeX, 4 eps figures included (macro epsf.tex), 1 figure available from request

Scientific paper

10.1088/0305-4470/30/14/017

We consider the action of the modular group $\Gamma (2)$ on the set of positive rational fractions. From this, we derive a model for a classification of fractional (as well as integer) Hall states which can be visualized on two ``visibility" diagrams, the first one being associated with even denominator fractions whereas the second one is linked to odd denominator fractions. We use this model to predict, among some interesting physical quantities, the relative ratios of the width of the different transversal resistivity plateaus. A numerical simulation of the tranversal resistivity plot based on this last prediction fits well with the present experimental data.

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