Composite Fermions and the Energy Gap in the Fractional Quantum Hall Effect

TL;DR

This paper calculates energy gaps in the fractional quantum Hall effect using composite fermion wave functions, showing how projection onto the lowest Landau level affects the energy contributions and supports the composite fermion theory.

Contribution

It provides detailed variational Monte Carlo calculations of energy gaps before and after projection, confirming the validity of the composite fermion approach.

Findings

Projected gaps agree with previous calculations

Projection localizes quasielectron charge

Energy contributions from Landau levels are clarified

Abstract

The energy gaps for the fractional quantum Hall effect at filling fractions 1/3, 1/5, and 1/7 have been calculated by variational Monte Carlo using Jain's composite fermion wave functions before and after projection onto the lowest Landau level. Before projection there is a contribution to the energy gaps from the first excited Landau level. After projection this contribution vanishes, the quasielectron charge becomes more localized, and the Coulomb energy contribution increases. The projected gaps agree well with previous calculations, lending support to the composite fermion theory.