Experimental constraints and a possible quantum Hall state at $\nu =5/2$

TL;DR

This paper explores possible topological orders at the quantum Hall state $ u=5/2$, proposing a new order compatible with experimental results that exhibits both Abelian properties and signatures similar to non-Abelian states.

Contribution

It introduces a topological order that reconciles conflicting experimental observations at $ u=5/2$, accommodating both upstream neutral modes and tunneling data.

Findings

Proposes a topological order compatible with multiple experimental results.

Identifies a state with both finite and zero spin polarizations.

Suggests signatures in interferometry similar to Pfaffian states.

Abstract

Several topological orders have been proposed to explain the quantum Hall plateau at $\nu=5/2$. The observation of an upstream neutral mode on the sample edge [Bid et al., Nature (London) 466, 585 (2010)] supports the non-Abelian anti-Pfaffian state. On the other hand, the tunneling experiments [Radu et al., Science 320, 899 (2008); Lin et al., Phys. Rev. B 85, 165321 (2012); Baer et al., arXiv:1405.0428] favor the Halperin 331 state which exhibits no upstream modes. We find a topological order, compatible with the results of both types of experiments. That order allows both finite and zero spin polarizations. It is Abelian but its signatures in Aharonov-Bohm interferometry can be similar to those of the Pfaffian and anti-Pfaffian states.