Statistics and dynamics in topological states of matter

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常规物质有着显著的不同。其中最引人注目的例子是分数量子霍尔效应中的分数电荷和统计。电荷分馏现在已被实验令人信服地证明。与此同时，对任意子的分数统计的直接实验观察构成了一个重大挑战。这一挑战最近引起了人们的广泛关注，因为在某些量子霍尔填充因子下，非阿贝尔任意子统计的可能性。非阿贝尔任意子的潜在应用和内在兴趣激发了人们在自然界中寻找这类粒子的尝试。该项目的第一个推力是由当前在这个方向上的实验所激发的，并将解决理论上提出的分数量子霍尔态的传输特征，这些量子霍尔态可用于检测。最新的实验提供了证据，支持在填充因子5/2的非极化或部分极化状态。可能的非极化和部分极化状态将被调查。第二个重点是手征系统中远离平衡的波动耗散定理的推导及其对从输运性质推导量子霍尔态结构的影响。第三个推力认识到量子霍尔液体是更广泛的拓扑绝缘体的代表。均匀拓扑绝缘体最近受到了极大的关注。对猝灭无序效应知之甚少。第三个推力地址金属-绝缘体的拓扑绝缘体的转变，重点是电子输运。PI还将研究基于拓扑绝缘体的纳米结构中的整流。这些方法将包括玻色化、凯尔迪什技术、任意子的代数理论、共形场论和其他分析和数值工具。大部分预算将用于支持研究生。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。PI将把新的发展纳入大学课程。他将在各个层面上参与学术界以外的外联活动。非技术性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。在这些受限系统中，电子形成的物质状态不能被描述为三维半导体中电子物质的一维和二维类似物。对这些新态及其相互转换的理解是凝聚态物理中的一个关键问题。分数量子霍尔效应就是一个突出的例子。在量子霍尔系统中，电子的行为就好像它们被分裂成几个部分，称为任意子，其电荷是电子电荷的一小部分，其性质与所有其他已知粒子截然不同。这些奇异的性质可能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任意子的许多问题仍然悬而未决。在某些重要的情况下，我们不知道当几个任意子重新排列时会发生什么。PI将在二维系统中研究这个问题，量子霍尔液体是一类更广泛的材料的代表，称为拓扑绝缘体。像普通的绝缘体一样，例如橡胶，拓扑绝缘体不会通过材料的内部导电。与普通绝缘体不同，拓扑绝缘体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制成的化合物。PI将研究真实的拓扑绝缘体材料的杂质和缺陷特性对拓扑绝缘体电子性质的影响。特别是，PI将解决一个可能性，建立一个最重要的元件之一的电路，二极管，从拓扑材料。该奖项支持几个教育活动。大部分预算将用于支持研究生。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。PI将把新的发展纳入大学课程。他将参与各级学术界以外的外联活动。

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.