Heat transport in topological matter

该奖项支持研究、教育和推广活动，目的是通过研究热量如何在拓扑物质中传输来实现对拓扑物质的基本理解。拓扑物质是一类新型材料，具有独特的坚固物理性能，对环境影响非常稳定。这一特性为测量科学中的许多潜在应用打开了大门，更重要的是，量子信息。这些应用与被称为任意子的难以捉摸的粒子的存在有关。我们通常认为电子没有组成部分。然而，在拓扑物质中，它们通常表现得好像是由称为任意子的复合粒子组成的。这些任意子有望用于构建量子计算机的基本组件，在量子计算机中，拓扑保护将有助于减少由于材料与环境相互作用而引入的不可避免的计算错误。在许多系统中，任意子的性质，甚至是否存在，仍然存在激烈的争论。这个奖项的主要重点是发展探索任何粒子存在和本质的方法。到目前为止，各种各样的电子实验已经提出并实施了这个目的。然而，电子工具有很大的局限性，不能在不导电的系统中工作。然而，这并不是热传递的限制。这个项目的关键思想包括关注热输运（而不是电子输运）来理解任何子，因此，拓扑物质。该奖项还支持PI的教育和推广活动，通过对本科生和研究生的研究培训，撰写教学评论文章，组织会议和研讨会，以及向K-12学生和公众推广，为美国科学，技术，工程和数学劳动力的发展做出贡献。该奖项支持旨在实现对拓扑物质热传输的基本理解的研究、教育和推广活动。在过去的几年里，在量化热导的实验检测方面取得了一些突破，包括对其分数量化的观察，这为非阿贝尔任意子的存在提供了证据。然而，拓扑热输运的许多方面仍然知之甚少。该项目有两个研究重点。第一部分着重讨论了热耗散和电荷与热输运的相互作用问题，这对实验数据的解释至关重要。第二个推力建立在任意子的热干涉测量的思想上。干涉测量法是探测分数统计量最直接的方法。在过去的两年中，带电任意子干涉测量的实验实现取得了巨大的进展。在这些最新发展的基础上，该项目将把任意子干涉测量的概念扩展到中性任意子和不支持电流的系统。该项目将解决带电和中性任意子干涉测量和超低温拓扑热输运中的几个相关问题。技术方法将结合共形场理论、Keldysh技术、任意子的代数理论、参照化、Bethe ansatz和其他工具。这项研究将受益于与魏茨曼科学研究所的实验人员的互动。该奖项还支持PI的教育和推广活动，通过对本科生和研究生的研究培训，撰写教学评论文章，组织会议和研讨会，以及向K-12学生和公众推广，为美国STEM劳动力的发展做出贡献。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports research, education, and outreach activities with a goal to achieve a fundamental understanding of topological matter by investigating how heat is transported within such matter. Topological matter is a new class of materials, which exhibit uniquely robust physical properties that are exceptionally stable to environmental effects. This property opens the door for many potential applications in measurement science, and more importantly, quantum information. These applications are related to the existence of elusive particles called anyons. We normally think of electrons as having no parts. Yet, in topological matter they often behave as if they were made of composite particles called anyons. These anyons are promising for building the fundamental components of a quantum computer, in which topological protection would help reduce otherwise unavoidable computational errors introduced by the material's interaction with its environment. The nature and even the existence of anyons in many systems remain hotly debated. The primary focus of this award is to develop ways to probe the existence and nature of anyons. So far, various electronic experiments have been proposed and implemented for this purpose. Yet, electronic tools have significant limitations and do not work in systems that do not conduct electricity. However, this is not a limitation for heat transport. The key idea of this project consists of focusing on heat transport (rather than electronic transport) to understand anyons, and hence, topological matter. This award also supports the PI's educational and outreach activities which contribute to the development of the US workforce in science, technology, engineering, and mathematics through research training of undergraduate and graduate students, writing pedagogical review articles, organization of conferences and workshops, and outreach to K-12 students and the general public.TECHNICAL SUMMARYThis award supports research, education, and outreach activities aimed at achieving a fundamental understanding of heat transport in topological matter. The last several years have witnessed several breakthroughs in the experimental detection of quantized thermal conductance, including the observation of its fractional quantization, which gives evidence of non-Abelian anyons. Yet, many aspects of topological heat transport remain poorly understood. The project has two research thrusts. The first one focuses on the problems of heat dissipation and the interplay of the charge and heat transport, which are crucial for the interpretation of the experimental data. The second thrust builds on the idea of thermal interferometry of anyons. Interferometry is the most direct way to probe fractional statistics. During the last two years, there has been dramatic progress in the experimental implementation of interferometry of charged anyons. Building on these recent developments, this project will extend the idea of anyonic interferometry to neutral anyons and to systems that do not support electric currents. The project will address several related problems in interferometry of charged and neutral anyons and in topological heat transport at ultra-low temperatures. The technical approaches will combine conformal field theory, Keldysh technique, algebraic theory of anyons, refermionization, Bethe ansatz, and other tools. The research will benefit from interaction with experimentalists from the Weizmann Institute of Science. This award also supports the PI's educational and outreach activities which contribute to the development of the STEM workforce in the US through research training of undergraduate and graduate students, writing pedagogical review articles, organization of conferences and workshops, and outreach to K-12 students and the general public.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.