Disorder and interaction in topological matter

该奖项支持拓扑量子材料理论的研究和教育。电子器件小型化方面的进展在现代技术将电子限制在纳米尺度的能力中达到了顶峰。这种约束导致了材料性质的急剧变化。一个引人注目的例子是分数量子霍尔效应，电子的行为就好像它们被分裂成几个更小的粒子，称为任意子。任意子的性质不同于自然界中任何其他粒子的性质，可以用于拓扑量子计算的潜在应用，拓扑量子计算独特地没有所有其他量子计算方法固有的错误。因此，拓扑量子计算机可以完成与更大的非拓扑量子计算机相同的任务，但量子位更少。该项目旨在了解任意子的性质，这是一个关键的开放问题。PI将与实验小组密切合作，并结合拓扑绝缘体领域的研究见解。拓扑绝缘体是一种新型材料，它不像传统的橡胶和塑料那样大量导电。然而，与橡胶和塑料不同的是，它们的表面形成导体。PI将研究在材料无序的情况下拓扑绝缘体表面的电流流动。除了研究之外，该奖项还支持一些教育和推广活动。大部分预算将用于支持研究生。其他活动将包括为本科生提供建议，在不同的学校年级进行拓展，以及组织一次科学会议。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。该奖项支持拓扑量子材料理论的研究和教育。拓扑材料的性质与其他材料截然不同，特别是在强相互作用或淬火无序的情况下。例如，库仑相互作用导致分数量子霍尔态的形成，电子分数化为任意子，这一理论预测为基础研究和应用开辟了非常重要的可能性，并刺激了许多实验工作。这个项目的第一个推动力部分是由最近的实验激发的，并专注于GaAs系统中第二朗道能级的分数量子霍尔态的性质。第一个推动力的另一个动机来自最近的突破性工作，该工作将拓扑绝缘体表面状态与二维半填充电子气体的理论思想联系起来。该项目探索了填充因子为5/2时粒子-空穴对称性缺失的相关物理现象，并用它来解释实验数据。这项研究解决了强相互作用对现有实验工具的影响，并与实验学家合作，旨在开发探测任意子的新方法。相对于弱淬火无序，拓扑性质是稳健的，但强无序可能导致显著的影响，如金属相的形成在三维拓扑绝缘体。该项目的第二个重点是研究这种不寻常金属的物理特性。该项目通过考虑具有分形表面的绝缘体，以及基于拓扑绝缘体的低维结构中的输运，探索了体与表面无序之间的交叉。除了研究之外，该奖项还支持一些教育和推广活动。大部分预算将用于支持研究生。其他活动将包括为本科生提供建议，在不同的学校年级进行拓展，以及组织一次科学会议。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。

NONTECHNICAL SUMMARYThis award supports research and education on the theory of topological quantum materials. Progress on electronic device miniaturization has culminated in the ability of modern technology to confine electrons at the nanoscale. Such confinement results in drastically changed material properties. A striking example is the fractional quantum Hall effect, where electrons behave as if they were split into several smaller particles, called anyons. The properties of anyons are unlike those of any other particles in nature, and can be used for potential applications in topological quantum computing, which is uniquely free of errors that are inherent in all other approaches to quantum computing. As a consequence, a topological quantum computer could accomplish the same tasks as a much larger non-topological quantum computer but with fewer qubits. The project aims at understanding the properties of anyons, which is a critical open problem. The PI will collaborate closely with experimental groups, and incorporate research insights from the field of topological insulators. Topological insulators are new materials that do not conduct electricity in the bulk like their conventional relatives rubber and plastic. However, in contrast to rubber and plastic, their surface forms a conductor. The PI will investigate the flow of electric current on the surfaces of topological insulators in the presence of material disorder. In addition to research, the award supports several educational and outreach activities. Most of the budget will be directed towards supporting graduate students. Other activities will involve advising undergraduate students, performing outreach at different school grade levels, and organizing a scientific conference. Graduate and undergraduate research on novel materials will contribute to the scientific education of the US workforce.TECHNICAL SUMMARYThis award supports research and education on the theory of topological quantum materials. The properties of topological materials are dramatically different from others, particularly in the presence of strong interactions, or quenched disorder. For example, Coulomb interaction leads to the formation of fractional quantum Hall states, where electrons fractionalize into anyons, a theoretical prediction that opens up possibilities of great importance for basic research and applications, and that has stimulated much experimental work. The first thrust of this project is motivated in part by recent experiments and focuses on the nature of the fractional quantum Hall states in the second Landau level in GaAs systems. The other motivation of the first thrust comes from the recent breakthrough work that connected theoretical ideas about surface states of topological insulators with 2D electron gases at half-filling. The project explores related physics in the absence of particle-hole symmetry at filling factor 5/2, and uses it to explain experimental data. The research addresses the effect of strong interactions on the existing experimental tools, and in collaboration with experimentalists' aims at developing new approaches to probing anyons.Topological properties are robust with respect to weak quenched disorder, but strong disorder may lead to striking effects, such as the formation of a metallic phase in 3D topological insulators. The second thrust of the project investigates the physics of that unusual metal. The project explores the crossover between bulk and surface disorder by considering insulators with fractal surfaces, as well as transport in low-dimensional structures based on topological insulators.In addition to research, the award supports several educational and outreach activities. Most of the budget will be directed towards supporting graduate students. Other activities will involve advising undergraduate students, performing outreach at different school grade levels, and organizing a scientific conference. Graduate and undergraduate research on novel materials will contribute to the scientific education of the US workforce.