Composite Fermion Theory, Edge Currents and the Fractional Quantum Hall Effect

TL;DR

This paper develops a mean field theory for composite fermion edge channels in quantum Hall systems, explaining fractional quantization of Hall conductance and discussing the nature of edge states in experiments.

Contribution

It introduces a theoretical framework linking composite fermion edge potentials to electron potentials, explaining experimental quantization and edge state behavior.

Findings

Reproduces observed fractional Hall conductance quantization

Provides a relation between composite fermion and electron potentials at edges

Discusses the nature of fractional edge states as Fermi or Luttinger liquids

Abstract

We present a mean field theory of composite fermion edge channel transport in the fractional and integer quantum Hall regimes. An expression relating the electro-chemical potentials of composite fermions at the edges of a sample to those of the corresponding electrons is obtained and a plausible form is assumed for the composite fermion Landau level energies near the edges. The theory yields the observed fractionally quantized Hall conductances and also explains other experimental results. We also discuss some experiments that are relevant to the question whether fractional edge states in real devices should be described as Fermi or Luttinger liquids.