Extracting the scaling dimension of quantum Hall quasiparticles from current correlations

TL;DR

This paper proposes a robust, simple method to determine the scaling dimension of quantum Hall quasiparticles from thermal noise measurements at a quantum point contact, aiding in distinguishing between candidate quantum Hall states.

Contribution

It introduces a minimally assumption-dependent scheme for extracting the quasiparticle scaling dimension from thermal tunneling noise, enhancing state characterization.

Findings

Scheme effectively extracts scaling dimension from noise data

Applicable to complex quantum Hall states with counterpropagating modes

Robust and model-independent approach

Abstract

Fractional quantum Hall quasiparticles are generally characterized by two quantum numbers: electric charge $Q$ and scaling dimension $\Delta$. For the simplest states (such as the Laughlin series) the scaling dimension determines the quasiparticle's anyonic statistics (the statistical phase $\theta=2\pi\Delta$). For more complicated states (featuring counterpropagating modes or non-Abelian statistics) knowing the scaling dimension is not enough to extract the quasiparticle statistics. Nevertheless, even in those cases knowing the scaling dimension facilitates distinguishing different candidate theories for describing the quantum Hall state at a particular filling (such as PH-Pfaffian and anti-Pfaffian at $\nu=5/2$). Here we propose a scheme for extracting the scaling dimension of quantum Hall quasiparticles from thermal tunneling noise produced at a quantum point contact. Our scheme makes only minimal assumptions about the edge structure and features the level of robustness, simplicity, and model independence comparable to extracting the quasiparticle charge from tunneling shot noise.