Anyon braiding and telegraph noise in a graphene interferometer

TL;DR

This paper demonstrates real-time observation of anyon braiding phases in fractional quantum Hall states using telegraph noise, providing a new method to characterize anyon exchange statistics.

Contribution

It introduces a novel approach to measure and analyze anyon braiding phases through three-state telegraph noise in quantum Hall interferometers.

Findings

Observed universal anyonic braiding phase in $ u=1/3$ and $4/3$ states.

Reconstructed phase-shifted Aharonov-Bohm oscillations from RTN.

Characterized anyon exchange statistics with methods extendable to non-abelian states.

Abstract

The search for anyons, quasiparticles with fractional charge and exotic exchange statistics, has inspired decades of condensed matter research. Quantum Hall interferometers enable direct observation of the anyon braiding phase via discrete interference phase jumps when the quasiparticle number changes. Here, we observe the universal anyonic braiding phase in both the $\nu = 1/3$ and $4/3$ fractional quantum Hall states by probing three-state random telegraph noise (RTN) in real-time. We find that the observed RTN stems from anyon quasiparticle number $n$ fluctuations and reconstruct three Aharonov-Bohm oscillation signals phase shifted by $2\pi/3$, corresponding to the three possible interference branches from braiding around $n$ (mod 3) anyons. Hence, we fully characterize the anyon exchange statistics using new methods that can readily extend to non-abelian states.