Noise on the Non-Abelian $\nu=5/2$ Fractional Quantum Hall Edge

TL;DR

This paper investigates how shot noise measurements at the edge of the $ u=5/2$ fractional quantum Hall state can differentiate between various non-Abelian topological orders, complementing thermal conductance data.

Contribution

It provides a method to distinguish between Pfaffian, anti-Pfaffian, and particle-hole-Pfaffian states using noise scaling and thermal conductance measurements.

Findings

Noise scaling varies with edge length for different states.

Thermal conductance combined with noise data can identify the topological order.

Distinct noise signatures help differentiate candidate states.

Abstract

The recent measurement of a half-integer thermal conductance for the $\nu=5/2$ fractional quantum Hall state has confirmed its non-Abelian nature, making the question of the underlying topological order highly intriguing. We analyze the shot noise at the edge of the three most prominent non-Abelian candidate states. We show that the noise scaling with respect to the edge length can, in combination with the thermal conductance, be used to experimentally distinguish between the Pfaffian, anti-Pfaffian, and particle-hole-Pfaffian edge structures.