Abstract
The topology-based explanation of the origin of the fractional quantum Hall effect is summarized. The cyclotron braid subgroups crucial for this approach are introduced in order to identify the origin of Laughlin correlations in 2D Hall systems. The so-called composite fermions are explained in terms of the homotopy cyclotron braids. Some new concept for fractional Chern insulator states is formulated in terms of the homotopy condition applied to the Berry field flux quantization.
Highlights
Topology plays increasing role in the development of current understanding of fundamentals in physics [1]
In the present paper we summarize the topological approach to Fractional Quantum Hall Effect (FQHE) via introduction of so-called cyclotron braid subgroups which help us in understanding of the Laughlin correlations specific for FQHE [13] [14]
After discovery of the integer quantum Hall effect (IQHE) in two dimensional electron system (2DEG) upon strong magnetic fields corresponding to complete fillings of succeeding Landau levels (LLs), the surprising observation of the fractional quantum Hall effect (FQHE) was reported at stronger magnetic fields resulting in the fractional fillings of the lowest Landau level (LLL)
Summary
Topology plays increasing role in the development of current understanding of fundamentals in physics [1]. The topological insight starts to be dominant in current understanding of Integer Quantum Hall Effect (IQHE) [8] and in rich applications of geometrical phase by Berry in various condensed matter problems [9] [10]. Application of the simple methods of the topological algebra in two dimensional spaces and in locally two dimensional ones, like a sphere or torus, is linked with the exceptional richness of the topological structure for multiparticle planar systems which is expressed by the π1 group of the related configuration spaces, called the braid groups [11]. In the present paper we summarize the topological approach to Fractional Quantum Hall Effect (FQHE) via introduction of so-called cyclotron braid subgroups which help us in understanding of the Laughlin correlations specific for FQHE [13] [14]
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