CAREER: Monopole Superconductivity and Ferromagnetism of Itinerant Electrons

本职业奖支持在金属材料研究中出现的异常状态和基本问题的理论研究和教育。一块金属含有许多电子，这些电子在运动并相互作用。量子力学控制着它们的集体行为，这可以产生新的物质状态，表现为电子秩序。考虑一个来自我们日常古典世界的秩序的例子，一队游泳运动员可以通过同步改变他们的身体形状来控制和改变他们的整体位置。量子系统中的类似现象被称为多体贝里相：由于量子力学效应，材料中的电子可以同步并表现出集体效应。电子可以被诱导成许多不同的有序状态，其中一些是以前没有观察到的。该项目通过探索秩序的数学描述及其物理结果来推进基本概念。该项目可能会导致开发一个新的量子计算平台。PI还将解决长期存在的问题，即揭示某些金属表现出磁性背后的微观机制。这是一个棘手的问题，因为一个普遍的理论假设是失败的，即在原子晶体中运动的电子可以被独立地考虑。事实上，任何一个电子的运动都与其他所有电子的运动密切相关。PI和她的研究团队将结合分析和数值方法来应对这一挑战。除了理论见解之外，该项目还可能导致利用这些强相关性现象的技术应用。该奖项将支持一系列教育和推广活动，从指导研究生、本科生和高中生，到开发与研究项目相一致的新课程材料，涵盖现代数学方法在凝聚态物理中的应用。PI还将针对Pre-K和K-12学生及其家长发起一项互动社区外展计划，旨在提高公众对量子物理学和研究前沿的兴趣和欣赏。本职业奖支持在拓扑、相互作用和强相关性的相互作用下产生的流动电子的新量子现象的理论研究和教育。具体来说，PI将专注于为新类别的多体拓扑状态开发一个理论框架，并在强相关多轨道系统中采用非微扰方法研究流动铁磁性。PI和她的团队将研究以单极谐波对称为特征的新型三维拓扑多体有序态，包括超导态和密度波态。粒子-粒子（库珀）配对，或粒子-空穴配对，继承了费米表面拓扑结构中的非平凡贝里相。它们的间隙函数不能在动量空间中全局定义，因此超出了基于球面谐波的旋转对称的标准实现。因此，无论特定的排序机制如何，它们都表现出拓扑保护的节点结构，并且只能用单极子调和函数来表征。流动铁磁性是基于费米表面不稳定性而不是局部自旋矩排序的移动电子的铁磁性。然而，它缺乏一个控制良好的弱耦合描述；对于轨道简并与铁磁性机制之间的关系，迄今还缺乏一个精确的答案，这主要是由于缺乏处理强磁波动的非摄动结果。PI和她的团队将开发非微扰方法，结合解析方法和无偏数值模拟，研究轨道简并在流动铁磁机制中的作用以及靠近铁磁跃迁的流动电子的强相关效应。该奖项将支持一系列教育和推广活动，从指导研究生、本科生和高中生，到开发与研究项目相一致的新课程材料，涵盖现代数学方法在凝聚态物理中的应用。PI还将针对Pre-K和K-12学生及其家长发起一项互动社区外展计划，旨在提高公众对量子物理学和研究前沿的兴趣和欣赏。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 CAREER award supports theoretical research and education in unusual states and fundamental questions that arise in the study of metallic materials. A piece of metal contains many electrons that are moving and interacting with each other. Quantum mechanics governs their collective behavior, which can give rise to new states of matter manifesting as electron order. Consider an example of order from our everyday classical world, a team of swimmers can control and change their position as a whole by performing a synchronized change in the shapes their bodies assume. An analogous phenomenon in quantum systems is called many-body Berry phases: due to quantum mechanical effects, electrons in a material can synchronize and exhibit collective effects. The electrons can be induced to organize in many different ordered states, some of which have not been observed before. This project advances fundamental concepts by exploring the mathematical description of order as well as its physical consequences. The project can potentially lead to developing a new platform for quantum computation.The PI will also tackle the long-standing problem of uncovering the microscopic mechanism behind the magnetism some metals exhibit. This is a formidable problem because of the failure of a common theoretical assumption, namely that electrons moving in a crystal of atoms can be considered independently. In fact, the motion of any one electron is strongly correlated with the motion of all others. The PI and her research team will combine analytic and numerical methods to tackle this challenge. Apart from theoretical insight, the project could lead to technological applications that harness these strong correlation phenomena.This award will enable a range of educational and outreach activities, from mentoring graduate, undergraduate, and high-school students, to developing new course materials aligned with the research project that cover the application of modern mathematical approaches in condensed matter physics. The PI will also initiate an interactive community outreach program targeting Pre-K and K-12 students and their parents, aimed at enhancing the public's interest in and appreciation of quantum physics and the research frontier.TECHNICAL SUMMARYThis CAREER award supports theoretical research and education in new quantum phenomena of itinerant electrons arising from the interplay of topology, interaction, and strong correlation. Specifically, the PI will focus on developing a theory framework for new classes of many-body topological states, and on a nonperturbative approach to itinerant ferromagnetism in strongly correlated multiorbital systems. The PI and her group will investigate novel classes of three-dimensional topological many-body ordering states characterized by monopole harmonic symmetries, including both superconducting and density-wave states. The particle-particle (Cooper) pairing, or, particle-hole pairing, inherits nontrivial Berry phases from Fermi surface topology. Their gap functions cannot be globally well-defined in momentum space, and thus go beyond the standard realization of rotational symmetry based on spherical harmonics. Consequently, they exhibit topologically protected nodal structures regardless of specific ordering mechanism and can only be characterized by monopole harmonic functions.Itinerant ferromagnetism is the ferromagnetism of mobile electrons based on Fermi surface instabilities rather than the ordering of local spin moments. However, it lacks a well-controlled weak-coupling description; a precise answer to the relation between orbital degeneracy and the mechanism of ferromagnetism has so far been lacking, mostly due to the lack of nonperturbative results for handling strong magnetic fluctuations. The PI and her group will develop nonperturbative methods, combining analytic approaches and unbiased numerical simulations, to study the role of orbital degeneracy in the mechanism of itinerant ferromagnetism and strong correlation effects of itinerant electrons close to ferromagnetic transitions.This award will enable a range of educational and outreach activities, from mentoring graduate, undergraduate, and high-school students, to developing new course materials aligned with the research project that cover the application of modern mathematical approaches in condensed matter physics. The PI will also initiate an interactive community outreach program targeting Pre-K and K-12 students and their parents, aimed at enhancing the public's interest in and appreciation of quantum physics and the research frontier.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.