[论文解读] Interferometric measurement of filling factor 5/2 quasiparticle charge

R. L. Willett, Michael J. Manfra+2 more|arXiv (Cornell University)|Jul 1, 2008

Quantum and electron transport phenomena被引用 3

一句话总结

本研究利用量子霍尔边缘态干涉仪测量了在5/2分数量子霍尔态下的准粒子电荷。通过在整数和分数量子霍尔填充因子下进行校准，发现在最低温度下出现周期性透射振荡，其周期对应于e/4电荷，以及出乎意料的e/2电荷，表明可能存在e/2准粒子或e/4准粒子的多次编织，对拓扑量子计算中的非阿贝尔统计具有重要意义。

ABSTRACT

A standing problem in low dimensional electron systems is the nature of the 5/2 fractional quantum Hall state: its elementary excitations are a focus for both elucidating the state's properties and as candidates in methods to perform topological quantum computation. Interferometric devices may be employed to manipulate and measure quantum Hall edge excitations. Here we use a small area edge state interferometer designed to observe quasiparticle interference effects. Oscillations consistent in detail with the Aharanov-Bohm effect are observed for integer and fractional quantum Hall states (filling factors 2, 5/3, and 7/3) with periods corresponding to their respective charges and magnetic field positions. With these as charge calibrations, at 5/2 filling factor and at lowest temperatures periodic transmission through the device consistent with quasiparticle charge e/4 is observed. The principal finding of this work is that in addtion to these e/4 oscillations, periodic structures corresponding to e/2 are also observed at 5/2 and at lowest temperatures. Properties of the e/4 and e/2 oscillations are examined with the device sensitivity sufficient to observe temperature evolution of the 5/2 quasiparticle interference. In the model of quasiparticle interference, this presence of an effective e/2 period may empirically reflect an e/2 quasiparticle charge, or may reflect multiple passes of the e/4 quasiparticle around the interferometer. These results are discussed within a picture of e/4 quasiparticle excitations potentially possessing non-Abelian statistics. These studies demonstrate the capacity to perform interferometry on 5/2 excitations and reveal properties important for understanding this state and its excitations.

研究动机与目标

• 利用干涉测量技术确定5/2分数量子霍尔态下的准粒子电荷。
• 通过在整数和分数量子霍尔填充因子（2、5/3、7/3）下使用已知准粒子电荷对干涉仪进行校准。
• 在低温条件下研究5/2填充因子下准粒子干涉的性质。
• 区分观测到的振荡中e/4与e/2准粒子的贡献。
• 评估研究结果对5/2准粒子非阿贝尔统计的影响。

提出的方法

• 制备了一个小面积的边缘态干涉仪，用于探测量子霍尔边缘激发态。
• 在填充因子2、5/3和7/3下测量干涉振荡，利用阿哈罗诺夫-玻姆效应校准准粒子电荷。
• 在5/2填充因子下精确控制磁场和温度运行干涉仪。
• 记录透射振荡随磁场的变化，以提取周期性并推断准粒子电荷。
• 进行温度依赖性测量，以研究干涉图案的演化。
• 使用理论模型解释数据中e/4与e/2周期性共存的现象。

实验结果

研究问题

• RQ1 通过干涉测量，5/2分数量子霍尔态下的准粒子电荷是多少？
• RQ2 为何在5/2填充因子下观测到e/2周期性的振荡，同时存在e/4周期性的振荡？
• RQ3 温度变化如何影响5/2处准粒子干涉的可见度和周期性？
• RQ4 观测到的e/2周期性是否可归因于e/4准粒子在干涉仪周围的多次编织，或源于内在的e/2准粒子？
• RQ5 干涉图案对5/2准粒子的非阿贝尔统计特性有何启示？

主要发现

• 在5/2填充因子下观测到周期性透射振荡，其周期对应于e/4电荷，与理论预测一致。
• 除e/4振荡外，在最低温度下还观测到具有e/2周期性的周期性结构。
• e/4与e/2振荡共存且具有温度依赖性，其可见度随温度降低而增强。
• e/2周期性的存在可能反映e/2准粒子的存在，或e/4准粒子在干涉仪周围多次编织的结果。
• 结果支持5/2态下存在e/4准粒子激发，并可能具有非阿贝尔统计特性。
• 干涉仪表现出足够的灵敏度，可解析准粒子干涉的温度演化，从而实现对任意统计特性的详细研究。