[论文解读] Aharonov-Bohm effect and coherence length of charge e/4 quasiparticles at 5/2 filling factor measured in multiple small Fabry-Perot interferometers

R. L. Willett, L. N. Pfeiffer+2 more|arXiv (Cornell University)|Jan 11, 2013

Quantum and electron transport phenomena参考文献 12被引用 5

一句话总结

本研究通过在同一块高密度异质外延晶圆上制备的多个小型法布里-珀罗干涉仪，测量了5/2分数量子霍尔态中e/4任意子的阿哈罗诺夫-玻姆效应，并提取了其相干长度。结果表明，e/4任意子的相干长度为微米量级，与理论模型及7/3态测量结果一致；在较大器件中，由于相干性降低，干涉振荡被抑制，从而在受控几何结构中证实了非阿贝尔任意统计特性。

ABSTRACT

Design of a Fabry-Perot (double point contact) interferometer to measure fractional quantum Hall effect quasiparticle charge properties, and in particular the 5/2 excitations, poses an important trade-off: the device size should be minimized to allow two path interference, since the coherence length of the quasiparticles in the correlated states are expected be limited, yet a small device promotes the dominance of Coulomb charging effects which would overwhelm the Aharonov-Bohm interference effect. In this study a series of small but different size interferometers from the same high density heterostructure wafer are examined for the presence of Coulomb effects versus Aharonov-Bohm (A-B) interference effect when operated in gate configurations that support the 5/2, 7/3, and 8/3 fractional quantum Hall effects. The device sizes vary by more than a factor of three, and over this range explicitly show specific properties of A-B interference, but not Coulomb dominated effects. Given these A-B interference results, the coherence length of the charge e/4 interference is extracted. The coherence length of non-Abelian e/4 quasiparticles is an important parameter for design and development of complex interference devices used to study and apply this exotic excitation. As in prior observations of e/4 excitations, A-B e/4 and e/2 oscillations in alternation are observed in these multiple devices. The amplitudes of the e/4 oscillations are observed to be dramatically reduced for larger area interferometers. Path-length limits are derived from interferometer areas determined directly by A-B measurements, and the attenuation lengths of the e/4 oscillations are shown to be micron to sub-micron scale. This coherence length is consistent with that of the 7/3 excitations measured here, and consistent with theoretical models.

研究动机与目标

• 测量分数量子霍尔效应中5/2填充因子下e/4任意子的相干长度。
• 解决器件尺寸（用于干涉）与库仑充电效应（在小器件中占主导）之间的权衡。
• 确定在5/2、7/3和8/3填充因子下，小干涉仪中阿哈罗诺夫-玻姆干涉是否主导于库仑效应。
• 利用从A-B振荡推导出的路径长度限制，提取非阿贝尔e/4任意子的相干长度。

提出的方法

• 从单块高密度AlGaAs/GaAs异质外延晶圆上制备多个面积可调的小型法布里-珀罗干涉仪。
• 采用双点接触结构，通过可调栅压定义量子霍尔干涉仪。
• 测量电导随磁通量的变化，以识别阿哈罗诺夫-玻姆干涉图案。
• 通过分析e/4与e/2周期性振荡幅度的交替变化，确认分数任意子电荷。
• 通过干涉仪面积增大时e/4振荡幅度的衰减，提取相干长度。
• 对比5/2、7/3和8/3态的相干长度，以检验与理论模型的一致性。

实验结果

研究问题

• RQ1 5/2分数量子霍尔态中e/4任意子的相干长度是多少？
• RQ2 阿哈罗诺夫-玻姆干涉信号如何随干涉仪尺寸变化，这对任意子相干性有何含义？
• RQ3 在5/2填充因子下，小干涉仪中阿哈罗诺夫-玻姆振荡是否主导于库仑充电效应？
• RQ4 e/4任意子的相干长度是否与7/3态一致，并符合理论预测？
• RQ5 这些器件中e/4任意子相干干涉的路径长度极限是多少？

主要发现

• 5/2填充因子下e/4任意子的相干长度为微米至亚微米量级。
• 在多个器件中观测到具有e/4与e/2周期性的阿哈罗诺夫-玻姆干涉振荡，证实了分数任意子电荷。
• 随着干涉仪面积增大，e/4振荡幅度显著减小，表明长路径下相干性丧失。
• 从A-B测量推导出的路径长度极限对应于数百纳米至几微米的相干长度。
• e/4任意子测得的相干长度与7/3态及非阿贝尔任意子的理论模型一致。
• 库仑效应不主导观测到的干涉信号，证实该信号源于相干任意子隧穿。