Laughlin's quasielectron as a non-local composite fermion

TL;DR

This paper analyzes Laughlin's quasielectron wavefunction, revealing it as a non-local composite fermion state with boundary effects and incorrect fractionalization, challenging its validity as a quasielectron model.

Contribution

It demonstrates that Laughlin's quasielectron is a non-local composite fermion state with boundary effects, questioning its suitability as a quasielectron wavefunction.

Findings

Laughlin's quasielectron exhibits non-local boundary properties.

It fractionalizes an incorrect spin, affecting braiding statistics.

The wavefunction is not a good candidate for a quasielectron model.

Abstract

We discuss the link between the quasielectron wavefunctions proposed by Laughlin and by Jain and show both analytically and numerically that Laughlin's quasielectron is a non-local composite fermion state. Composite-fermion states are typically discussed in terms of the composite-fermion Landau levels (also known as Lambda levels). In standard composite-fermion quasielectron wavefunctions the excited Lambda levels have sub-extensive occupation numbers. However, once the Laughlin's quasielectron is reformulated as a composite fermion, an overall logarithmic occupation of the first Lambda level is made apparent, which includes orbitals that are localized at the boundary of the droplet. Even though the wavefunction proposed by Laughlin features a localised quasielectron with well-defined fractional charge, it exhibits some non-trivial boundary properties which motivate our interpretation of Laughlin's quasielectron as a non-local object. This has an important physical consequence: Laughlin's quasielectron fractionalizes an incorrect spin, deeply related to the anyonic braiding statistics. We conclude that Laughlin's quasielectron is not a good candidate for a quasielectron wavefunction.