Topological Heat Transport

非技术总结该奖项支持拓扑量子材料的理论研究和教育，这是一类特殊的材料，具有非常稳定的性能。这个特性被称为拓扑保护。量子力学是拓扑材料的特殊性质的原因。例如，考虑电子，它实际上没有组成粒子。在某些拓扑物质中，它们看起来好像已经分裂成粒子，称为任意子，它们也携带均匀分布的原始电荷。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。PI将开发理解量子拓扑材料及其特性的理论方法。最近的实验突破揭示了热量如何通过拓扑物质传播。该项目的主要目标是提供量子热输运的理论理解，并解决现有理论框架与二维量子拓扑物质行为的最新实验数据之间的紧张关系。该研究将推进对拓扑物质和量子输运的基本理解，这两个方向对已成为国家优先事项的量子科学和技术至关重要。通过为研究生和本科生提供研究和教育机会，包括与领先的实验学家合作，该奖项的学生将接受培训，最终加入现代量子科学和技术的未来劳动力队伍。技术概述该奖项支持拓扑量子材料的理论研究和教育，重点是热传输和中性模式的相关物理。拓扑物质中任意子的非阿贝尔分数统计在量子信息存储和处理中有重要的应用。对非阿贝尔统计和拓扑物质中的许多其他现象的理解需要实验获得中性激发，这来自于热输运实验。第一个研究方向是由最近的实验发展的动机，旨在实现量子霍尔液体的边缘，包括上游中性模式的影响，热平衡和运输的理论理解。密切相关的第二个方向地址在GaAs和相关系统的第二个朗道水平的量子霍尔态知之甚少。填充因子为5/2的半整数量子化热导的观测结果有力地支持了在第二朗道能级中存在非阿贝尔任意子。然而，许多开放的问题仍然存在，包括现有的实验结果和数值之间的明显冲突。这项研究建立在最近的实验结果和儿子的突破性工作的关系，二维电子气体和拓扑绝缘体。目的是使5/2态的理论与实验相一致。第三个研究方向集中在新开发的拓扑系统与中性模式，但没有收费模式。所采用的方法将包括分析和数值工具相结合。该研究将推进拓扑物质和量子传输的基础知识，这两个方向对量子科学和技术至关重要，已成为国家优先事项。通过为研究生和本科生提供研究和教育机会，包括与领先的实验学家合作，该奖项的学生将接受培训，最终加入现代量子科学和技术的未来劳动力队伍。该奖项反映了NSF的法定使命，并通过使用基金会的智力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 theoretical research and education on topological quantum materials, which are a special class of materials that have been bestowed with exceptionally stable properties. That feature is known as topological protection. Quantum mechanics is responsible for the exceptional properties of topological materials. Consider, for example, electrons, which in reality do not have constituent particles. In certain topological matter, they appear as if they have split into particles, called anyons, which also carry an equally distributed fraction of the original electric charge. 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 PI will develop theoretical approaches for understanding quantum topological materials and their properties. Recent breakthroughs in experiments have uncovered how heat travels through topological matter. A major goal of this project consists of providing a theoretical understanding of quantum heat transport, and also resolving tensions between the existing theoretical framework and the newest experimental data on the behavior of quantum topological matter in two dimensions.The research will advance fundamental understanding of topological matter and quantum transport, both of which are directions of crucial importance for quantum science and technology that have become a national priority. Through research and education opportunities for graduate and undergraduate students, which include collaborations with leading experimentalists, students under the award will be trained to eventually join the future workforce in modern quantum science and technology.TECHNICAL SUMMARYThis award supports theoretical research and education on topological quantum materials with a focus on heat transport and the related physics of neutral modes. The non-Abelian fractional statistics of anyons in topological matter may find significant applications in quantum information storage and processing. The understanding of non-Abelian statistics and many other phenomena in topological matter requires experimental access to neutral excitations, which comes from thermal transport experiments. The first research direction is motivated by recent experimental developments and aims at achieving theoretical understanding of thermal equilibration and transport on the edges of quantum Hall liquids, including the effects of upstream neutral modes. The closely related second direction addresses poorly understood quantum Hall states in the second Landau level in GaAs and related systems. The observation of half-integer quantized thermal conductance at filling factor 5/2 strongly supports the existence of non-Abelian anyons in the second Landau level. Yet, many open problems remain, including an apparent conflict between the existing experimental results and numerics. The research builds upon recent experimental results and the breakthrough work by Son on the relation of 2D electron gases and topological insulators. The objective is to reconcile the theory of the 5/2 state with experiments. A third research direction focuses on newly developed topological systems with neutral modes but without charged modes. The methods employed will include a combination of analytical and numerical tools. The research will advance fundamental knowledge of topological matter and quantum transport, both of which are directions of crucial importance for quantum science and technology that have become a national priority. Through research and education opportunities for graduate and undergraduate students, which include collaborations with leading experimentalists, students under the award will be trained to eventually join the future workforce in modern quantum science and technology.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.