Quasiparticle tunneling in the Moore-Read fractional quantum Hall State

TL;DR

This paper investigates quasiparticle tunneling in the Moore-Read fractional quantum Hall state, revealing that e/4 quasiholes have significantly higher tunneling amplitudes than e/2 quasiholes, with implications for experimental observations.

Contribution

It provides the first detailed calculation of tunneling matrix elements for e/4 and e/2 quasiholes in the Moore-Read state, highlighting their relative tunneling strengths.

Findings

e/4 quasiholes have larger tunneling amplitudes than e/2 quasiholes

The ratio of tunneling amplitudes is mainly due to charge differences

Long-range Coulomb interactions weakly affect the tunneling ratio

Abstract

In fractional quantum Hall systems, quasiparticles of fractional charge can tunnel between the edges at a quantum point contact. Such tunneling (or backscattering) processes contribute to charge transport, and provide information on both the charge and statistics of the quasiparticles involved. Here we study quasiparticle tunneling in the Moore-Read state, in which quasiparticles of charge e/4 (non-Abelian) and e/2 (Abelian) may co-exist and both contribute to edge transport. On a disk geometry, we calculate the matrix elements for e/2 and e/4 quasiholes to tunnel through the bulk of the Moore-Read state, in an attempt to understand their relative importance. We find the tunneling amplitude for charge e/2 quasihole is exponentially smaller than that for charge e/4 quasihole, and the ratio between them can be (partially) attributed to their charge difference. We find that including long-range Coulomb interaction only has a weak effect on the ratio. We discuss briefly the relevance of these results to recent tunneling and interferometry experiments at filling factor nu=5/2.