The effects of non-abelian statistics on two-terminal shot noise in a quantum Hall liquid in the Pfaffian state

TL;DR

This paper investigates how non-Abelian statistics influence shot noise in a quantum Hall Pfaffian state, revealing subtle effects at higher perturbation orders that could be experimentally detectable.

Contribution

It demonstrates that higher-order calculations of shot noise can reveal signatures of non-Abelian statistics in quantum Hall systems, and proposes multi-terminal measurements for clearer detection.

Findings

Fractional charge of quasiparticles can be extracted at first order.

Non-Abelian statistics effects appear at higher-order noise calculations.

Multi-terminal noise measurements may provide stronger signatures of non-Abelian statistics.

Abstract

We study non-equilibrium noise in the tunnelling current between the edges of a quantum Hall liquid in the Pfaffian state, which is a strong candidate for the plateau at $\nu=5/2$. To first non-vanishing order in perturbation theory (in the tunneling amplitude) we find that one can extract the value of the fractional charge of the tunnelling quasiparticles. We note however that no direct information about non-abelian statistics can be retrieved at this level. If we go to higher-order in the perturbative calculation of the non-equilibrium shot noise, we find effects due to non-Abelian statistics. They are subtle, but eventually may have an experimental signature on the frequency dependent shot noise. We suggest how multi-terminal noise measurements might yield a more dramatic signature of non-Abelian statistics and develop some of the relevant formalism.