Electronic Many-body States with Topological Order

****技术摘要****局限于GaAs/AlGaAs异质结构的二维电子气为研究降维系统中强电子-电子相互作用所带来的突现现象提供了一个模型平台。最近的理论工作表明，二维电子系统具有以前未预料到的拓扑秩序和不寻常的准粒子统计的物质的新相。拓扑秩序的概念已经扩展到许多新的材料，它现在渗透到现代凝聚态物理。我们的工作重点是二维电子气体的基础科学问题，如诱导各种感兴趣的基态之间的跃迁和寻找新的拓扑不变量。通过对现代凝聚态物理的研究，以及现代半导体加工、低能级测量和低温设备使用方面的培训，本项目将为研究生未来的学术或工业生涯做好良好的准备。将向本科生介绍凝聚态物理中使用的概念和技术。*****非技术摘要****分数量子霍尔效应的研究揭示了相互作用的量子力学电子排列自己的迷人规则。最近出现的一种观点是，某些分数态可能具有一种称为拓扑秩序的新型内部自由度。拓扑秩序的概念可能允许以新的方式存储和操纵量子信息，并且它现在已经在概念上应用于许多新型凝聚态材料。在这个项目中，我们将研究清洁二维电子气体中的隐藏秩序。这些实验将融合现代半导体加工、纳米物理学和最先进的低温技术。该项目将支持培养一名现代凝聚态物理博士研究生，该学科历来为学术界和高科技行业的载体提供了优秀的培训。

****Technical Abstract****The two-dimensional electron gas confined to GaAs/AlGaAs heterostructures provides a model platform for the study of emergent phenomena brought about by strong electron-electron interactions in systems with reduced dimensionality. Recent theoretical work suggests that the two-dimensional electron system hosts novel phases of matter with previously unanticipated topological order and unusual quasiparticle statistics. The concept of topological order has been extended to many novel materials and it now permeates modern condensed matter physics. Our work focuses on questions of fundamental science of the two-dimensional electron gas such as inducing transitions between the various ground states of interest and the search for novel topological invariants. This project will constitute excellent preparation for a graduate student for his/her future academic or industrial career through the study of modern condensed matter physics and training in modern semiconductor processing, in conducting low level measurements, and in the use of cryogenic equipment. Undergraduate students will be introduced to concepts and techniques used in condensed matter physics.*****Non-Technical Abstract****Studies of the fractional quantum Hall effect reveal fascinating rules according to which the interacting quantum mechanical electrons arrange themselves. It has recently come to the fore that it is possible that certain fractional states may have a new type of internal degree of freedom called topological order. The concept of topological order may allow storing and manipulating quantum information in new ways and it has now conceptually been applied to many novel condensed matter materials. For this project we will study this hidden order in clean two-dimensional electron gases. The experiments will be at the confluence of modern semiconductor processing, nanophysics, and state-of-the art cryogenic technology. This project will support the education of a doctoral student in modern condensed matter physics which has historically provided excellent training for carriers both in academia as well as in high tech industries.