Explanation of fractional hierarchy observed experimentally in higher Landau levels

TL;DR

This paper explains the unique fractional quantum Hall effect hierarchy in higher Landau levels by deriving filling rates and using topological arguments, aligning theory with experimental observations.

Contribution

It systematically derives fractional filling rates in higher Landau levels and explains the observed hierarchy using topology-based commensurability arguments.

Findings

Hierarchy in higher Landau levels matches experimental data.

Fractional structures are explained by pairing criteria at half fillings.

Paucity of fractional states in higher levels is clarified.

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.