CAREER: "Geometry, topology and symmetry in strongly correlated materials"

职业：“强相关材料中的几何、拓扑和对称性”

• 批准号: 1455368
• 负责人: Rahul Roy
• 金额: $ 47.5万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-07-01 至 2020-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1455368&HistoricalAwards=false
• 关键词: CAREER; Geometry; topology; symmetry; strongly

NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education aimed to study the properties of certain materials called topological phases. These are states of matter which unlike most others have physical properties that are robust and are not affected by deformation and impurities. This leads to the possibility that some topological phases can be profitably used to store information and manipulate its flow in ways that are not possible in today's computers. Most kinds of materials that might lend themselves to these applications have so far been engineered in conditions which are quite hard to achieve under ordinary conditions; they require very high magnetic fields and very low temperatures. The PI will perform theoretical research aimed to understand better the physics of the materials that host topological phases of electrons and to explore the conditions that most favor the realization of topological phases in the absence of large magnetic fields. Robust phenomena similar to those that occur in electronic topological phases are also predicted to occur in systems which are acted on by a periodic external perturbation. The PI aims to understand these better and to classify the types of behavior that are possible. This research may contribute to eventual useful applications in metrology and in computation, and may help develop and improve open source quantum many-body computer programs. It could also lead to the development of new photonic devices.The PI will work with existing outreach programs at University of California, Los Angeles to introduce new experiments to the pre-collegiate curriculum. The PI will tap into an existing "Research Experience for Undergraduates" program to involve undergraduate students in research and build interest in physics among female students through the Clare Booth Luce foundation. The PI will continue development of course materials on topological phenomena and also help in dissemination of new ideas through introductory talks and a journal club. TECHNICAL SUMMARYThis CAREER award supports theoretical research and education on strongly correlated systems focusing on the interplay among geometry, symmetry and topology. Topological phases lie outside the conventional paradigm of organizing phases by symmetry; nevertheless, they hold potential for enabling new device technologies and realizing quantum computation by virtue of their novel electronic properties. To advance understanding of topological phases, the PI will focus on the following thrusts: 1.) Developing a unified theory of the fractional quantum Hall effect and fractional Chern insulators. By incorporating aspects of the quantum geometry of the single particle Hilbert space in these systems, the PI proposes to design and develop new analytic and numerical tools which should aid the search for more experimentally accessible realizations of quantum Hall phenomena. 2.) Investigating the role of crystal symmetries in topological phenomena. Using topological arguments, the PI plans to improve constraints on symmetry enforced degeneracies and complete the classification of short-range entangled topological states with crystal symmetries. 3.) Exploring topological phenomena in periodically driven systems. The PI will aim to characterize these topologically robust phenomena, study the effects of interactions, the physical consequences of the classification, and connect these with experiments. The PI's education and outreach activities will promote diversity and improve science education at the elementary, undergraduate and graduate levels. The PI will work with existing outreach programs at the University of California, Los Angeles to introduce new experiments to the pre-collegiate curriculum. The PI will involve undergraduates in summer research programs through an existing "Research Experience for Undergraduates" program and build interest in physics among female students through the Clare Booth Luce foundation. The PI will continue developing course materials on topological phenomena. New developments in ongoing research will be disseminated through introductory talks and a journal club.

非技术摘要这一职业奖支持理论研究和教育，旨在研究某些称为拓扑阶段的材料的特性。这些状态与大多数其他物质不同，其物理特性稳健，并且不受变形和杂质的影响。这导致可能有可能利用某些拓扑阶段来存储信息并以当今计算机不可能的方式操纵其流量。到目前为止，在普通条件下很难实现的条件下，大多数可能会借此应用这些应用的材料已经设计了；它们需要非常高的磁场和非常低的温度。 PI将进行理论研究，旨在更好地了解电子的拓扑阶段的物理，并探索在没有大磁场的情况下最有利于实现拓扑阶段的条件。与电子拓扑阶段相似的鲁棒现象也预计会发生在由周期性外部扰动作用的系统中。 PI旨在更好地理解这些问题并分类可能的行为类型。这项研究可能有助于最终有用的计量和计算应用程序，并可能有助于开发和改善开源量子多体计算机程序。这也可能导致新的光子设备的开发。PI将与加利福尼亚大学洛杉矶分校的现有外展计划合作，向学前班课程介绍新的实验。 PI将利用现有的“本科生研究经验”计划，使本科生通过Clare Booth Luce Foundation参与研究并建立对女学生的兴趣。 PI将继续开发有关拓扑现象的课程材料，并通过介绍性谈判和期刊俱乐部帮助传播新思想。技术摘要这一职业奖支持理论研究和教育有关强烈相关的系统，重点是几何，对称性和拓扑之间的相互作用。拓扑阶段位于对称性组织阶段的常规范式之外。然而，它们具有实现新设备技术并通过其新型电子特性实现量子计算的潜力。为了促进对拓扑阶段的理解，PI将重点放在以下推力上：1。）制定分数量子霍尔效应和分数Chern绝缘子的统一理论。通过在这些系统中纳入单个粒子希尔伯特空间的量子几何形状的各个方面，PI提议设计和开发新的分析和数值工具，这些工具应有助于寻找对量子厅现象的更多实验可访问的实现。 2.）研究晶体对称性在拓扑现象中的作用。使用拓扑论点，PI计划改善对对称性强制性变性的约束，并完成具有晶体对称性的短距离纠缠拓扑状态的分类。 3.）探索定期驱动系统中的拓扑现象。 PI将旨在表征这些拓扑稳健的现象，研究相互作用的影响，分类的物理后果，并将其与实验联系起来。 PI的教育和外展活动将促进多样性，并改善小学，本科和研究生级别的科学教育。 PI将与加州大学洛杉矶分校的现有外展计划合作，将新实验介绍给大学前课程。 PI将通过现有的“本科生研究经验”计划参与夏季研究计划，并通过Clare Booth Luce Foundation对女学生的物理学兴趣。 PI将继续开发有关拓扑现象的课程材料。正在进行的研究的新发展将通过入门演讲和期刊俱乐部进行传播。