1997/01/30 by Yvon Georgelin, Y. M. Georgelin, Thierry Masson +1 · 1 citation
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum optics and atomic interactions #Topological Materials and Phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1088/0305-4470/30/14/017
17 pages, plain TeX, 4 eps figures included (macro epsf.tex), 1 figure available from request
arxiv created 1997/01/30 · openalex publication_date 1997/07/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We consider the action of the modular group 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.