[Paper Review] Slow quasiparticle dynamics and anyonic statistics in a fractional quantum Hall Fabry-Pérot interferometer

Noah L. Samuelson, Liam A. Cohen+6 more|arXiv (Cornell University)|Mar 28, 2024

Quantum and electron transport phenomena4 citations

TL;DR

This study demonstrates slow quasiparticle dynamics and direct observation of anyonic statistics in a monolayer graphene fractional quantum Hall Fabry-Pérot interferometer at $ν=1/3$. By independently tuning interferometer area and quasiparticle number, the authors measure a phase slip magnitude of $\Delta\theta \approx 2\pi/3$, confirming Abelian anyon statistics, while revealing quasiparticle equilibration times exceeding 20 minutes, indicating long-lived topological charge stability on hour-long timescales.

ABSTRACT

Anyons are particles with fractional exchange statistics that emerge as elementary excitations of fractional quantum Hall phases. Experimentally, their exchange statistics can be measured in the edge-state Fabry-Pérot interferometer. In these devices, the presence of $N_{qp}$ localized anyons in the bulk contributes a phase $N_{qp}θ_a$ to the interference signal. Here we report the observation of large, hysteretic phase jumps in a monolayer graphene Fabry-Pérot interferometer at $ν=1/3$. When the filling factor is increased from $ν<1/3$ towards the center of the plateau, we observe phase slips with magnitude $Δθ\approx 2π/3$, consistent with the addition of individual quasiparticles to the interferometer bulk. In contrast to prior work, however, the phase slips occur as instantaneous jumps in the interference signal, indicative of quasiparticle equilibration times exceeding 20 minutes. We use this long timescale to investigate the effect of changes in interferometer area $A_I$ and $N_{QP}$ independently at fixed magnetic field, revealing a striking memory effect in the phase slip magnitude. In particular, as the $ν=1/3$ plateau is approached from higher filling, we observed phase slips with $Δθ$ significantly larger than $2π/3$ over the same range of gate voltage where quantized jumps are seen for increasing $ν$. We discuss this asymmetry in terms of bulk-edge coupling of quasiparticles localized near the edge or in the bulk, and argue that this effect can be qualitatively reconciled with theoretical expectations for strongly interacting quasiparticles in the presence of weak disorder and strongly nonequilibrium charge dynamics. Our results highlight the key role played by charge dynamics on signatures of the anyon phase, and demonstrate that fractional quasiparticles can be indefinitely localized in nonequilibrium configurations.

Motivation & Objective

• To directly probe anyonic statistics in a graphene-based fractional quantum Hall system using a Fabry-Pérot interferometer.
• To investigate quasiparticle dynamics and equilibration times in a mesoscopic quantum Hall device.
• To disentangle topological phase contributions from bulk-edge coupling effects in interferometric measurements.
• To observe and characterize individual quasiparticle tunneling events in real time via phase slips.
• To determine the statistical exchange phase $\theta_a$ in a graphene heterostructure and assess its stability over long timescales.

Proposed method

• Fabrication of a dual-graphite-gated monolayer graphene Fabry-Pérot interferometer with tunable area and quasiparticle number.
• Use of quantum point contacts (QPCs) to control quasiparticle injection and extraction into the interferometer loop.
• Simultaneous tuning of plunger gate voltage ($V_C$) and magnetic field ($B$) to independently vary interferometer area ($A_I$) and quasiparticle number ($N_{qp}$).
• Measurement of conductance oscillations to extract the interferometer phase $\theta$, with phase slips indicating discrete changes in $N_{qp}$.
• Analysis of phase slip magnitudes and temporal sequences to infer quasiparticle equilibration dynamics and charge configuration stability.
• Comparison of charge fingerprints across phase slip sequences to rule out simple two-state switching and infer correlated quasiparticle removal.

Figure 1: Fabry-Pérot interference in the $\nu=1/3$ state (A) Schematic of the dual-graphite gated edge state Fabry-Pérot interferometer. The gates defining the interferometer are labeled C, NW, SW, NE, SE and P. Edge states are formed in the monolayer graphene around the center-gated region (C) and

Experimental results

Research questions

• RQ1 What is the value of the anyonic statistical phase $\theta_a$ in a graphene-based $\nu=1/3$ fractional quantum Hall state?
• RQ2 How do quasiparticle tunneling and equilibration dynamics manifest in real time within a mesoscopic interferometer?
• RQ3 Can the interferometer phase be precisely controlled and monitored by independently tuning area and quasiparticle number?
• RQ4 Do phase slips correspond to single or correlated removal of quasiparticles, and what does this imply about many-body anyon dynamics?
• RQ5 How stable is the topological charge of the interferometer over long timescales, and what limits equilibration?

Key findings

• The measured phase slip magnitude is $\Delta\theta \approx 2\pi/3$, consistent with the expected statistical exchange phase for Abelian anyons in the $\nu=1/3$ state.
• Individual quasiparticle tunneling events manifest as instantaneous and irreversible phase slips, indicating quasiparticle equilibration times exceeding 20 minutes in some cases.
• The interferometer phase remains approximately constant over time, with an average of one phase slip per additional flux quantum above 8.94 T, despite stochastic timing.
• Charge fingerprints from sequences separated by two phase slips show distinct curve shapes, ruling out simple two-state switching and suggesting multiple distinct charge configurations.
• The system exhibits long-lived topological charge stability, with the average 'topological charge' remaining constant over hour-long timescales.
• The absence of phase slips during repeated $V_C$ ramps in certain regimes confirms that phase slips are not artifacts of gate voltage cycling, but reflect genuine quasiparticle dynamics.

Figure 2: Irreversible charging dynamics. (A) $G_{D}$ vs. $V_{C}$ as the magnetic field is swept from 8.88T to 9T. The latter half of the measurement shows many sudden phase jumps, beginning at $B=8.95T$ and continuing until the end of the sweep. (B) $G_{D}$ vs. $V_{C}$ as the magnetic field is swep