Pfaffian and fragmented states at nu=5/2 in quantum Hall droplets

TL;DR

This paper explores electron pairing and state fragmentation in quantum Hall droplets at filling factor 5/2, revealing potential challenges in observing non-abelian quasi-particles due to shape-dependent state breakdown.

Contribution

It demonstrates that electron pairing at nu=5/2 can occur in quantum dots and shows how external potential shape influences state stability and fragmentation.

Findings

Electron pairing can occur in quantum dots at nu=5/2.

State fragmentation depends on the shape of the external potential.

Fragmentation may hinder detection of non-abelian quasi-particles.

Abstract

When a gas of electrons is confined to two dimensions, application of a strong magnetic field may lead to startling phenomena such as emergence of electron pairing. According to a theory this manifests itself as appearance of the fractional quantum Hall effect with a quantized conductivity at an unusual half-integer nu=5/2 Landau level filling. Here we show that similar electron pairing may occur in quantum dots where the gas of electrons is trapped by external electric potentials into small quantum Hall droplets. However, we also find theoretical and experimental evidence that, depending on the shape of the external potential, the paired electron state can break down, which leads to a fragmentation of charge and spin densities into incompressible domains. The fragmentation of the quantum Hall states could be an issue in the proposed experiments that aim to probe for non-abelian quasi-particle characteristics of the nu=5/2 quantum Hall state.