Limits of Applicability of the Composite Fermion Model.

Janusz E Jacak

doi:10.3390/ma14154267

Abstract

The popular model of composite fermions, proposed in order to rationalize FQHE, were insufficient in view of recent experimental observations in graphene monolayer and bilayer, in higher Landau levels in GaAs and in so-called enigmatic FQHE states in the lowest Landau level of GaAs. The specific FQHE hierarchy in double Hall systems of GaAs 2DES and graphene also cannot be explained in the framework of composite fermions. We identify the limits of the usability of the composite fermion model by means of topological methods, which elucidate the phenomenological assumptions in composite fermion structure and admit further development of FQHE understanding. We demonstrate how to generalize these ideas in order to explain experimentally observed FQHE phenomena, going beyond the explanation ability of the conventional composite fermion model.

Highlights

The fractional quantum Hall effect (FQHE) was discovered experimentally in 1982 byTsui, Stormer and Gossard in GaAs 2DES [1], shortly after the experimental discovery of the integer quantum Hall effect (IQHE) in 1980 by von Klitzing in a 2D electron system in a perpendicular magnetic field [2]
The experimental achievements have been distinguished with the Nobel prizes and have opened a wide discipline of condensed matter related to Hall physics in 2D systems, including graphene and topological insulators [3], study of which rapidly flourished in the past few years
Various routes towards explanation of queer discrete structure of FQHE hierarchy have been proposed, like the multiparticle wave functions for the corresponding correlated states suggested by Laughlin in 1983 [4]

Summary

Introduction

The fractional quantum Hall effect (FQHE) was discovered experimentally in 1982 by. Tsui, Stormer and Gossard in GaAs 2DES [1], shortly after the experimental discovery of the integer quantum Hall effect (IQHE) in 1980 by von Klitzing in a 2D electron system in a perpendicular magnetic field [2]. The Laughlin function, proposed without a derivation in a phenomenological manner [4,11], was the most illuminating theoretical discovery and gave rise to various phenomenological models intended to decipher the physics behind correlations of electrons at FQHE This multiparticle wave function proposed by Laughlin for N interacting electrons on the plane exposed to a strong quantizing perpendicular magnetic field was the simple generalization of the Slater function for N noninteracting 2D electrons at the field B = B0, at which the degeneracy of Landau levels (LLs) N0(B0) = N, where. It has been proved that it is impossible to derive this function within local quantum mechanics, and topological methods are required [15] This is connected with the fact that the FQHE collective state is not a conventional phase. We will show how to generalize the CF model

Laughlin Function and CF Model

Cyclotron Braid Group Generators and Wave-Functions for Homotopy Phases

Multiparticle Wave Functions for FQHE States in the LLL of GaAs

Simple Examples

Homotopy Invariants in Higher LLs and in Bilayer Hall Systems