## 20230630 Partitioning of diluted anyons reveals their braiding statistics

Partitioning of diluted anyons reveals their braiding statistics

Changki Hong

Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute

of Science, Rehovot, Israel.

Fractional quantum Hall systems host anyons that carry fractional charges and obey their anyonic

statistics. Here we describe a new kind of process named ‘time-domain braiding’. The experiment is based on

a ‘two-quantum point contact’ configuration fabricated in 2D electrons confined in a high-purity GaAs/AlGaAs

heterostructure. In this setup, the first quantum point contact (QPC) strongly diluted a full beam of incoming

anyons (here, e/3 quasiparticles), which then impinges, after travelling 2m, on weakly backscattering second

QPC (inset in the figure). Time-domain braiding of thermally excited particle-hole pairs in the second QPC

occurs only in the presence of incoming diluted anyons. This time-interference braiding process involves twotime

events: a dilute anyon arrives before the thermal particle-hole excitation and a dilute anyon arriving after

the excitation. This time-domain braiding strongly affects the auto-correlation (shot noise) of the backscattered

current fluctuations in the second QPC [1].

The theoretical description of the time-domain anyons braiding and the expected auto-correlation in the

second QPC is based on the chiral Luttinger liquid theory. Correlations also consider the contribution of trivial

partitioning events of the diluted beam in the second QPC [2].

We carried out measurements in both: integer (=3) and fractional (=1/3 and =2/5) regimes. In the

integer regime, the results agreed with the conventional partitioning of particles, leading to a Fano factor, F=1.

On the other hand, the calculated Fano factor for =1/3 and =2/5 outer edge were F=3.27 – with an excellent

agreement with the experimental results. A separation of 20m between the two QPCs led to a trivial Fano

factor, suggesting a decoherence of the dilute beam. Our work provides a relatively straightforward method to

observe the anyonic braiding statistics of exotic quantum Hall states without using complex interferometry

experiments.

[1] J.-Y. M Lee, C. Hong, T. Alkalay, et al., Nature 617, 277 (2023).

[2] J.-Y. M Lee, H.-S. Sim, Nat. Comm. 13, 6660 (2022).