Explanation of the odd structure of fractional Hall states in higher Landau levels and filling ratios with even denominators

TL;DR

This paper systematically derives the structure of fractional fillings in higher Landau levels, explaining the scarcity of fractional states compared to the zeroth level and identifying even denominator fillings with pairing criteria.

Contribution

It introduces a topology-based hierarchy for fractional fillings in higher Landau levels, aligning with experimental data and explaining the structure's oddness.

Findings

Hierarchy of fractional fillings derived for higher Landau levels.

Identification of even denominator filling fractions and pairing criteria.

Explanation for fewer fractional states in higher Landau levels.

Abstract

The structure of fractional fillings of higher Landau levels including spin subbands is systematically derived for the first time. Using topology-type commensurability arguments for 2D charged system in the presence of strong quantizing magnetic field, a hierarchy of fillings in the higher Landau levels for FQHE and for other correlated states is determined in perfect agreement with the experimental observations. The relative paucity of fractional structure in the higher Landau levels in contrast to the plethora of filling factors for FQHE in the zeroth Landau level is explained. The filling fractions with even denominators in consecutive LLs were also identified together with the criterion for particle pairing.