[论文解读] 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 phenomena被引用 4

一句话总结

本研究在$ν=1/3$的单层石墨烯分数量子霍尔法布里-珀罗干涉仪中，展示了准粒子动力学的缓慢特性，并首次直接观测到任意任何任何统计行为。通过独立调节干涉仪面积和准粒子数，作者测得相位滑移大小为$\Delta\theta \approx 2\pi/3$，证实了阿贝尔任意统计行为，同时揭示准粒子弛豫时间超过20分钟，表明在小时量级时间尺度上拓扑电荷具有长期稳定性。

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.

研究动机与目标

• 利用法布里-珀罗干涉仪直接探测基于石墨烯的分数量子霍尔系统中的任意统计行为。
• 研究介观量子霍尔器件中准粒子的动力学与弛豫时间特性。
• 在干涉测量中分离拓扑相位贡献与体-边耦合效应的影响。
• 通过相位滑移实现实时光学观测并表征单个准粒子隧穿事件。
• 测定石墨烯异质结中的统计交换相$\theta_a$，并评估其在长时间尺度上的稳定性。

提出的方法

• 制备具有可调面积和准粒子数的双石墨烯背栅单层石墨烯法布里-珀罗干涉仪。
• 利用量子点接触（QPCs）控制准粒子注入与提取至干涉仪环路。
• 同时调节栅压（$V_C$）与磁场（$B$），以独立改变干涉仪面积（$A_I$）与准粒子数（$N_{qp}$）。
• 通过测量电导振荡提取干涉仪相位$\theta$，相位滑移表明$N_{qp}$发生离散变化。
• 分析相位滑移的大小与时间序列，推断准粒子弛豫动力学与电荷构型稳定性。
• 比较相位滑移序列中的电荷指纹，排除简单双态切换模型，推断准粒子的关联移除行为。

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

实验结果

研究问题

• RQ1 在基于石墨烯的$\nu=1/3$分数量子霍尔态中，任意统计相位$\theta_a$的值是多少？
• RQ2 在介观干涉仪中，准粒子隧穿与弛豫动力学如何在真实时间中表现？
• RQ3 是否可通过独立调节面积与准粒子数精确控制并监测干涉仪相位？
• RQ4 相位滑移是否对应单个或关联的准粒子移除？这对多体任意统计动力学有何含义？
• RQ5 干涉仪的拓扑电荷在长时间尺度上有多稳定？其弛豫过程受何因素限制？

主要发现

• 测得的相位滑移大小为$\Delta\theta \approx 2\pi/3$，与$\nu=1/3$态中阿贝尔任意子的预期统计交换相一致。
• 单个准粒子隧穿事件表现为瞬时且不可逆的相位滑移，表明在某些情况下准粒子弛豫时间超过20分钟。
• 尽管相位滑移时间随机，干涉仪相位在长时间内保持近似恒定，平均每增加一个磁通量子，相位滑移约1次（在8.94 T以上）。
• 相隔两次相位滑移的序列所呈现的电荷指纹具有明显不同的曲线形状，排除了简单双态切换模型，表明存在多种不同的电荷构型。
• 系统表现出长期的拓扑电荷稳定性，平均‘拓扑电荷’在小时量级时间尺度上保持恒定。
• 在某些区域重复$V_C$扫描过程中未观察到相位滑移，证实相位滑移并非栅压循环的伪影，而是真实准粒子动力学的体现。

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