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

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.