Abstract
The topological explanation of the origin of Laughlin correlations in 2D charged systems under strong magnetic fields is formulated. Formal, self-consistent mathematical model of originally identified cyclotron braid subgroups is given in order to fully describe fundamentals of fractional quantum Hall effect, retrieve Laughlin correlations and point physical conditions which stand behind mysterious composite fermion structure. The new complete implementation of composite fermion basing on the first principles, without involving any artificial constructions (with flux-tubes or vortices) supply an explanation of previous models of composite fermions. Presented approach can lead to some corrections of numerical results in energy minimizations made within the traditional formulation of composite fermion model. Authors also identify the relations of FQHE in cyclotron braid terms within newly developing area of topological insulators and optical lattices. The prerequisites needed for formation of the fractional state are identified beyond the traditionally assumed factors, like the flat band condition and the interaction presence. The role of high mobility of carriers is highlighted in agreement with the experimental observations. Description, in terms of cyclotron braid subgroups, of the nature of yet unexplained novel experiments in Hall 2D systems including graphene is provided as well.
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