Composite Fermions and the Fractional Quantum Hall Effect: Essential Role of the Pseudopotential

TL;DR

This paper explains how the success of the mean field composite Fermion model in fractional quantum Hall systems depends on the short-range nature of the Coulomb pseudopotential in the lowest Landau level, clarifying its applicability.

Contribution

It identifies the specific pseudopotential conditions under which the composite Fermion mean field picture accurately predicts low-lying states.

Findings

Success of the CF picture is due to short-range Coulomb pseudopotential behavior.

The class of pseudopotentials for which the CF model works is characterized.

The framework explains successes and failures in various quantum Hall scenarios.

Abstract

The mean field (MF) composite Fermion (CF) picture successfully predicts the band of low lying angular momentum multiplets of fractional quantum Hall systems for any value of the magnetic field. This success cannot be attributed to a cancellation between Coulomb and Chern--Simons interactions between fluctuations beyond the mean field. It results instead from the short range behavior of the Coulomb pseudopotential in the lowest Landau level (LL). The class of pseudopotentials for which the MFCF picture is successful can be defined, and used to explain the success or failure of the picture in different cases (e.g. excited LL's, charged magneto-excitons, and Laughlin quasiparticles in a CF hierarchy picture).