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，拓扑量子材料是一种特殊类别的材料，被赋予了异常稳定的性质。这一功能被称为拓扑保护。量子力学是拓扑材料具有特殊性质的原因。例如，考虑电子，它实际上没有组成粒子。在某些拓扑物质中，它们看起来就像是分裂成了粒子，称为任意子，这些粒子也携带着原始电荷的均匀分布部分。这些任意子在构建量子计算机的基本组件方面很有希望，在量子计算机中，拓扑保护将有助于减少材料与环境相互作用带来的不可避免的计算误差。PI将为理解量子拓扑材料及其性质开发理论方法。最近的实验突破揭示了热是如何在拓扑物质中传播的。该项目的一个主要目标是提供对量子热输运的理论理解，并解决现有理论框架与有关量子拓扑物质行为的最新实验数据之间的紧张关系。这项研究将促进对拓扑物质和量子输运的基本理解，这两个方向都是量子科学和技术的关键方向，已成为国家重点。通过为研究生和本科生提供研究和教育机会，包括与领先的实验者合作，获得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大军。技术总结该奖项支持拓扑量子材料的理论研究和教育，重点是热传输和相关的中性模式物理。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具有重要的应用价值。为了理解非阿贝尔统计和拓扑物质中的许多其他现象，需要通过实验获得中性激发，而中性激发来自热输运实验。第一个研究方向受到最近实验发展的推动，旨在从理论上理解量子霍尔液体边缘的热平衡和输运，包括上游中性模的影响。密切相关的第二个方向解决了在砷化镓及相关系统中鲜为人知的第二朗道能级中的量子霍尔态。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第二朗道能级中非阿贝尔任意子的存在。然而，仍然存在许多悬而未决的问题，包括现有的实验结果与数值计算之间的明显冲突。这项研究建立在最近的实验结果和Son在2D电子气与拓扑绝缘体关系方面的突破性工作的基础上。其目的是使5/2态的理论与实验相一致。第三个研究方向集中在新发展的具有中性模式但没有带电模式的拓扑系统。所采用的方法将包括分析工具和数值工具的结合。这项研究将推进拓扑物质和量子输运的基础知识，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，包括与领先的实验者合作，获得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大军。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.