Neutral Fermion Excitations in the Moore-Read state at \nu=5/2

TL;DR

This paper provides numerical evidence for neutral fermion excitations in the Moore-Read state at rac{5}{2}, highlighting their gapped or gapless nature depending on quasiparticle configurations, supporting non-Abelian statistics.

Contribution

It demonstrates the existence and characteristics of neutral fermion modes in the Moore-Read state through numerical analysis, revealing their signatures and implications for non-Abelian anyons.

Findings

Neutral fermion mode has two minima observable via photoluminescence.

Neutral fermion is gapped with odd particle number systems.

Neutral fermion becomes gapless with two quasiparticles, confirming non-Abelian statistics.

Abstract

We present evidence supporting the weakly paired Moore-Read phase in the half-filled second Landau level, focusing on some of the qualitative features of its excitations. Based on numerical studies, we show that systems with odd particle number at the flux $N_\phi=2N-3$ can be interpreted as a neutral fermion mode of one unpaired fermion, which is gapped. The mode is found to have two distinct minima, providing a signature that could be observed by photoluminescence. In the presence of two quasiparticles the same neutral fermion excitation is shown to be gapless, confirming expectations for non-Abelian statistics of the Ising model with degenerate fusion channels 1 and $\psi$.