Edge States and Interferometers in the Pfaffian and anti-Pfaffian States

TL;DR

This paper analyzes tunneling currents in a quantum Hall system at filling fraction 5/2, comparing the Pfaffian and anti-Pfaffian states, revealing their non-Abelian properties and quantitative differences in voltage and temperature dependence.

Contribution

It provides a detailed quantitative comparison of tunneling behaviors in the Pfaffian and anti-Pfaffian states at 5/2 filling, highlighting their non-Abelian signatures.

Findings

Both states show an even-odd effect indicating non-Abelian statistics.

The two states exhibit similar qualitative behavior but differ quantitatively in voltage and temperature dependence.

The study advances understanding of edge states and interferometry in quantum Hall systems.

Abstract

We compute the tunneling current in a double point contact geometry of a Quantum Hall system at filling fraction $\nu=5/2$, as function of voltage and temeprature, in the weak tunneling regime. We quantitatively compare two possible candidates for the state at $\nu=5/2$: the Moore-Read Pfaffian state, and its particle-hole conjugate, the anti-Pfaffian. We find that both possibilities exhibit the same qualitative behavior, and both have an even-odd effect that reflects their non-Abelian nature, but differ quantitatively in their voltage and temperature dependance.