Identification of the Fractional quantum Hall edge modes by density oscillations

TL;DR

This paper investigates fractional quantum Hall edge modes, especially neutral fermionic modes, using density oscillations and Jack polynomials, aiding their identification and understanding in finite systems and interferometry.

Contribution

It introduces a method to distinguish bosonic and fermionic edge modes via density oscillations and applies it to identify modes near edge reconstruction in FQH states.

Findings

Density oscillations differentiate bosonic and fermionic edge modes.

Method successfully identifies edge modes near edge reconstruction.

Extrapolated edge velocities and coherence lengths for interferometry applications.

Abstract

The neutral fermionic edge mode is essential to the non-Abelian topological property and its experimental detection in $Z_k$ fractional quantum Hall (FQH) state for $k > 1$. Usually, the identification of the edge modes in a finite size system is difficult, especially near the region of the edge reconstruction, due to mixing with the bosonic edge mode and the bulk states as well. We study the edge-mode excitations of the Moore-Read (MR) and Read-Rezayi (RR) states by using Jack polynomials in the truncated subspace. It is found that the electron density, as a detector, has marked different behaviors between the bosonic and fermionic edge modes. As an application, it helps us to identify them near the edge reconstruction and in the RR edge spectrum. On the other hand, we systematically study the edge excitations for the RR state, extrapolate the edge velocities and their related coherence length and temperature in the interferometer experiments.