Single-electron tunneling in the fractional quantum Hall effect regime

TL;DR

This paper reviews a mean-field approach to the fractional quantum Hall effect, focusing on single-electron tunneling through quantum dots in high magnetic fields, and relates the spectra to the integer QHE via a charge substitution.

Contribution

It applies the Greiter-Wilczek adiabatic principle to analyze single-electron tunneling in fractional QHE, connecting the spectra to the Fock-Darwin spectrum with fractional charge substitution.

Findings

Spectrum related to Fock-Darwin spectrum with fractional charge

Implications for Aharonov-Bohm oscillation periodicity

Analysis of the addition spectrum in quantum dots

Abstract

A recent mean-field approach to the fractional quantum Hall effect (QHE) is reviewed, with a special emphasis on the application to single-electron tunneling through a quantum dot in a high magnetic field. The theory is based on the adiabatic principle of Greiter and Wilczek, which maps an incompressible state in the integer QHE on the fractional QHE. The single-particle contribution to the addition spectrum is analyzed, for a quantum dot with a parabolic confining potential. The spectrum is shown to be related to the Fock-Darwin spectrum in the integer QHE, upon substitution of the electron charge by the fractional quasiparticle charge. Implications for the periodicity of the Aharonov-Bohm oscillations in the conductance are discussed.