Explanation of fractional hierarchy observed experimentally in higher Landau levels

2014/05/11 by Janusz Jacak, Jacak, Janusz, Lucjan Jacak +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Control Systems Design #FOS: Physical sciences #Fractional Differential Equations Solutions #General Physics (physics.gen-ph) #physics.gen-ph

paper · pdf · doi:10.48550/arxiv.1405.2598

openalex publication_date 2014/05/11 · arxiv created 2014/08/20 · arxiv updated 2014/08/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The puzzle of an odd structure of fractional fillings for FQHE in higher Landau levels not repeating the hierarchy from the lowest Landau level is solved. The fractional filling rates for correlated states in higher Landau levels including spin subbands are systematically derived for the first time. Using topology-type commensurability arguments the hierarchy in higher Landau level fillings is determined in perfect agreement with the experimental observations. The relative paucity of fractional structure in higher Landau levels is explained and the criterion for pairing in states at half fillings and for other even-denominator rates of consecutive Landau levels is formulated.

Related

• Explanation of the odd structure of fractional Hall states in higher Landau levels and filling ratios with even denominators
• Hierarchy of fillings for FQHE in monolayer and in bilayer graphene: Explanation of ν=-(1)/(2) fractional quantum Hall state in bilayer graphene
• Test of the hierarchical theory for the FQHE
• Pairing of Composite Fermions, Laughlin Correlations, and the Fractional Quantum Hall Hierarchy
• An Unsettled Issue in the Theory of the Half-Filled Landau Level