Statistics and dynamics in topological states of matter

物质拓扑态的统计和动力学

• 批准号: 1205715
• 负责人: Dmitri Feldman
• 金额: $ 31.13万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1205715&HistoricalAwards=false
• 关键词: Statistics; dynamics; topological; states; matter

TECHNICAL SUMMARYThis award supports research on the theory of topological quantum materials and related educational activities. The properties of quantum correlated systems are strikingly different from conventional matter. One of the most dramatic examples is the fractional charge and statistics in the fractional quantum Hall effect. Charge fractionalization is by now convincingly proven by experiment. At the same time, a direct experimental observation of the fractional statistics of anyons poses a major challenge. This challenge has recently attracted much attention because of a possibility of non-Abelian anyonic statistics at some quantum Hall filling factors. Possible applications as well as intrinsic interest of non-Abelian anyons have stimulated attempts to find such particles in nature. The first thrust of this project is motivated by current experiments in this direction and will address transport signatures of theoretically proposed fractional quantum Hall states which can be used for their detection. Latest experiments provide evidence in support of an unpolarized or partially polarized state at the filling factor 5/2. Possible unpolarized and partially polarized states will be investigated. The second thrust focuses on the derivation of far-from-equilibrium fluctuation-dissipation theorems in chiral systems and their implications for deducing the structure of quantum Hall states from transport properties. The third thrust recognizes that Quantum Hall liquids are representatives of a much broader class of topological insulators. Homogeneous topological insulators have recently received great attention. Less is known about quenched disorder effects. The third thrust addresses metal-insulator transitions in topological insulators with a focus on electronic transport. The PI will also investigate rectification in nanostructures based on topological insulators. The methods will include bosonization, the Keldysh technique, the algebraic theory of anyons, conformal field theory and other analytical and numerical tools.This award supports several educational activities. Most of the budget will be directed for graduate student support. The PI will also involve undergraduates in his research. Graduate and undergraduate research on novel materials will contribute to the scientific education of the US workforce. The PI will incorporate new developments in university courses. He will participate in outreach beyond the academic community on various levels.NONTECHNICAL SUMMARYThis award provides support for research on the theory of topological quantum materials and related educational activities. Modern technology allows confining semiconductors on the nanoscale in one or two dimensions. The states of matter formed by electrons in these confined systems cannot be described as one- and two-dimensional analogs of electronic matter in three-dimensional semiconductors. The understanding of those novel states and the transformations among them is a key problem in condensed matter physics. The fractional quantum Hall effect provides a striking example. In quantum Hall systems electrons behave as though they were split into several pieces, called anyons, whose charge is a fraction of the electron charge and whose properties are dramatically different from all other known particles. These exotic properties may open a road to a practical implementation of quantum computing. Many questions about anyons in quantum Hall systems remain open. In some important situations it is not known what happens when several are rearranged anyons. The PI will investigate this issue in two-dimensional systems in the first thrust of the research.Quantum Hall liquids are representatives of a much broader class of materials called topological insulators. Like ordinary insulators, for example rubber, topological insulators do not conduct electricity though the interior of the material. Unlike ordinary insulators, topological insulators are able to conduct electricity on their edges or boundaries through the formation of a new state of matter. Among the known topological insulators are compounds made of the elements bismuth and selenium, and bismuth and tellurium. The PI will investigate the effects of impurities and imperfections characteristic of real topological insulator materials on the electronic properties of topological insulators. In particular, the PI will address a possibility to build one of the most important elements of electric circuits, a diode, from topological materials.This award supports several educational activities. Most of the budget will be directed for graduate student support. The PI will also involve undergraduates in his research. Graduate and undergraduate research on novel materials will contribute to the scientific education of the US workforce. The PI will incorporate new developments in university courses. He will participate in outreach beyond the academic community on various levels.

技术总结该奖项支持拓扑量子材料理论的研究和相关的教育活动。量子关联系统的性质与传统物质有着惊人的不同。最戏剧性的例子之一是分数量子霍尔效应中的分数电荷和统计。到目前为止，电荷分馏得到了令人信服的实验证明。与此同时，对任意子分数统计的直接实验观测构成了一个重大挑战。这一挑战最近引起了人们的极大关注，因为在某些量子霍尔填充因子上存在非阿贝尔任意子统计的可能性。可能的应用以及非阿贝尔任意子的内在兴趣刺激了人们在自然界中寻找此类粒子的尝试。这个项目的第一个推力是受到目前这一方向的实验的推动，并将解决理论上提出的分数量子霍尔态的传输特征，这些特征可以用于检测它们。最新的实验提供了支持填充因子为5/2的非偏振态或部分偏振态的证据。可能的非偏振态和部分偏振态将被研究。第二个重点是手性系统中远离平衡的涨落-耗散定理的推导，以及它们对从输运性质推断量子霍尔态结构的启示。第三个推力承认，量子霍尔液体是更广泛类别的拓扑绝缘体的代表。均质拓扑绝缘子最近受到了极大的关注。人们对猝灭的无序效应知之甚少。第三个推力涉及拓扑绝缘体中的金属-绝缘体转变，重点是电子传输。PI还将研究基于拓扑绝缘体的纳米结构的整流。这些方法将包括玻色化、凯尔德什技术、任意子的代数理论、保形场理论和其他分析和数值工具。该奖项支持几个教育活动。大部分预算将直接用于研究生资助。PI还将让本科生参与他的研究。研究生和本科生对新材料的研究将有助于美国劳动力的科学教育。国际和平研究所将在大学课程中纳入新的发展。他将在不同层面上参与学术界以外的活动。非技术总结该奖项为拓扑量子材料理论的研究和相关教育活动提供支持。现代技术允许将半导体限制在一维或二维的纳米尺度上。电子在这些受限系统中形成的物质的状态不能描述为三维半导体中电子物质的一维和二维类似物。理解这些新的态以及它们之间的转换是凝聚态物理学中的一个关键问题。分数量子霍尔效应就是一个明显的例子。在量子霍尔系统中，电子的行为就像它们被分成几个部分，称为任意子，它们的电荷是电子电荷的一小部分，其性质与所有其他已知的粒子截然不同。这些奇特的性质可能会为量子计算的实际实现开辟一条道路。关于量子霍尔系统中的任意子的许多问题仍然悬而未决。在一些重要的情况下，当几个任意子被重新排列时，会发生什么是未知的。作为研究的第一要旨，PI将在二维系统中研究这一问题。量子霍尔液体是一种更广泛的被称为拓扑绝缘体的材料的代表。与普通绝缘体(例如橡胶)一样，拓扑型绝缘体不通过材料内部导电。与普通绝缘子不同，拓扑绝缘子能够通过形成新的物质状态在其边缘或边界上导电。在已知的拓扑绝缘体中，有由元素铋和硒以及铋和碲组成的化合物。PI将研究真实拓扑绝缘子材料的杂质和缺陷特性对拓扑绝缘子电子性能的影响。特别是，PI将解决用拓扑材料建造电路中最重要的元件之一-二极管的可能性。该奖项支持几项教育活动。大部分预算将直接用于研究生资助。PI还将让本科生参与他的研究。研究生和本科生对新材料的研究将有助于美国劳动力的科学教育。国际和平研究所将在大学课程中纳入新的发展。他将在不同层面上参与学术界以外的活动。