Identifying the $\nu=\frac{5}{2}$ topological order through charge transport measurements

TL;DR

This paper proposes an experimental setup to determine the topological order of the $ u=5/2$ quantum Hall state by measuring electric conductance in a device interfacing different filling factors, helping to identify specific topological phases.

Contribution

It introduces a novel conductance measurement method to distinguish between competing topological orders of the $ u=5/2$ state, including Pfaffian, anti-Pfaffian, and particle-hole symmetric states.

Findings

Conductance measurements can identify the particle-hole symmetric Pfaffian order.

The setup can differentiate between Moore-Read and Anti-Pfaffian topological orders.

Recent thermal measurements support the proposed identification method.

Abstract

We propose an experiment to identify the topological order of the $\nu=\frac{5}{2}$ state through a measurement of the electric conductance of a mesoscopic device. Our setup is based on interfacing $\nu=2, \ \frac{5}{2}$ and $3$ in the same device. Its conductance can unambiguously establish or rule out the particle-hole symmetric Pfaffian topological order, which is supported by recent thermal measurements. Additionally, it distinguishes between the Moore-Read and Anti-Pfaffian topological orders, which are favored by numerical calculations.