Explanation of puzzling FQHE at the filling fraction 3/4 in a band-hole 2D system in GaAs.

A recent experiment revealed an unexpected FQHE at filling fraction 3/4 in a GaAs 2D hole system, which contradicts the composite fermion model prediction and the observation of a compressible Hall metal-type state in a twin 2D electron system in GaAs at the same filling fraction 3/4 at almost same other conditions. This finding challenges conventional effective single-quasiparticle model for FQHE exposing its limitations. We explain this experimental observation within a multiparticle approach based on a topological cyclotron commensurability criterion. This allows to generalize Laughlin function for filling fractions from the complete FQHE hierarchy including observable FQHE states at even denominator fractions. The topological multiparticle approach helps to decipher a structure of composite fermions and provides their generalization for so-called enigmatic states including even denominator filling fractions, and also for quantum fractional Hall-type behavior in Chern topological insulators without a magnetic field.