Cross-Correlation Investigation of Anyon Statistics in the $\nu=1/3$ and $2/5$ Fractional Quantum Hall States

TL;DR

This paper investigates the signatures of anyon braiding statistics in fractional quantum Hall states through cross-correlation measurements, revealing negative correlations consistent with anyon exchange phases and proposing methods to distinguish their origins.

Contribution

It provides experimental evidence of anyon statistics in $ u=1/3$ and $ u=2/5$ states using cross-correlation measurements and discusses how to differentiate between fractional braiding and Andreev-like mechanisms.

Findings

Negative cross-correlations observed for $ u=1/3$ and $ u=2/5$ quasiparticles.

Quantitative link between cross-correlation value and exchange phase is complex.

Source balance adjustments can distinguish between braiding and Andreev mechanisms.

Abstract

Recent pioneering works have set the stage for exploring anyon braiding statistics from negative current cross-correlations along two intersecting quasiparticle beams. In such a dual-source - analyzer quantum point contact setup, also referred to as 'collider', the anyon exchange phase of fractional quantum Hall quasiparticles is predicted to be imprinted into the cross-correlations characterized by an effective Fano-factor $P$. In the case of symmetric incoming quasiparticle beams, conventional fermions result in a vanishing $P$. In marked contrast, we observe signatures of anyon statistics in the negative $P$ found both for the $e/3$ Laughlin quasiparticles at filling factor $\nu=1/3$ ($P\approx-2$, corroborating previous findings), and for the $e/5$ quasiparticles in the hierarchical state $\nu=2/5$ ($P\approx-1$). Nevertheless, we argue that the quantitative connection between numerical value of $P\neq0$ and specific fractional exchange phase is hampered by the influence of the analyzer conductance dependence on the voltages used to generate the quasiparticles. Finally, we address the important challenge how to distinguish at $\nu=1/3$ between negative cross-correlations induced by a fractional braid phase, and those resulting from a different Andreev-like mechanism. Although with symmetric sources $P$ does not exhibit signatures of a crossover when the analyzer is progressively detuned to favor Andreev processes, we demonstrate that changing the balance between sources provides a mean to discriminate between the two mechanisms.