Explanation of fractional hierarchy observed experimentally in higher Landau levels

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.