Heat transport in topological matter

该奖项支持研究，教育和推广活动，旨在通过调查热量如何在此类物质中传输来实现对拓扑物质的基本理解。拓扑物质是一类新的材料，它具有独特的物理性质，对环境影响非常稳定。这种性质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。我们通常认为电子是没有部件的。然而，在拓扑物质中，它们常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，其中拓扑保护将有助于减少材料与环境相互作用所引入的不可避免的计算错误。在许多系统中，任意子的性质甚至存在性仍然是激烈争论的话题。该奖项的主要重点是开发探索任意子的存在和性质的方法。到目前为止，已经提出了各种电子实验，并实现了这一目的。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，这不是热传输的限制。该项目的核心思想是关注热输运（而不是电子输运），以理解任意子，从而理解拓扑物质。 该奖项还支持PI的教育和推广活动，这些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了贡献。以及旨在对拓扑物质中的热传输进行基本了解的外展活动。在过去的几年里，在量子化热导的实验检测方面取得了一些突破，包括观察到它的分数量子化，这提供了非阿贝尔任意子的证据。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。第一个集中在热耗散的问题和相互作用的电荷和热传输，这是至关重要的实验数据的解释。第二个推力建立在任意子热干涉测量的想法上。干涉测量是研究分数统计量最直接的方法。 在过去的两年里，在带电任意子干涉测量的实验实施方面取得了巨大的进展。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。技术方法将结合联合收割机共形场论，Keldysh技术，任意子的代数理论，量子化，Bethe anomaly和其他工具。这项研究将受益于与魏茨曼科学研究所实验人员的互动。该奖项还支持PI的教育和推广活动，这些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，与K的联系该奖项反映了NSF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。

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.