Anyonic statistics and slow quasiparticle dynamics in a graphene fractional quantum Hall interferometer

Anyons are two dimensional particles with fractional exchange statistics that emerge as elementary excitations of fractional quantum Hall phases. Experimentally, anyonic statistics manifest directly in the edge-state Fabry-P\'erot interferometer geometry, where the presence of Nqp localized anyons in the interferometer bulk contributes a phase Nqp θₐ to the observed interference pattern, where θₐ is twice the statistical exchange phase. Here, we report a measurement of θₐ in a monolayer graphene Fabry-P\'erot interferometer at ν = 1/3. We find a preponderance of phase slips with magnitudes Δ θ ≈ 2 π / 3, confirming the result of past experiments in GaAs quantum wells and consistent with expectations for the tunneling of Abelian anyons into the interferometer bulk. In contrast to prior work, however, single anyon tunneling events manifest as instantaneous and irreversible phase slips, indicative of quasiparticle equilibration times exceeding 20 minutes in some cases. We use the discrepancy between the quasiparticle equilibration rate and our measurement speed to vary the interferometer area and Nqp independently, allowing us to precisely determine the interferometer phase and monitor the entry and exit of individual anyons to the interferometer loop in the time domain. Besides providing a replication of previous interferometric measurements sensitive to θₐ in GaAs, our results bring anyon dynamics into the experimental regime and suggest that the average `topological charge' of a mesoscopic quantum Hall device can be held constant over hour long timescales.