CAREER: Monopole Superconductivity and Ferromagnetism of Itinerant Electrons

非技术性总结该职业奖支持在金属材料研究中出现的不寻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。量子力学支配着它们的集体行为，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经典世界的秩序的例子，一组游泳者可以通过同步改变他们身体呈现的形状来控制和改变他们的整体位置。量子系统中的一个类似现象被称为多体贝瑞相：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，其中一些以前没有被观察到。该项目通过探索秩序的数学描述及其物理后果来推进基本概念。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的磁性背后的微观机制。这是一个棘手的问题，因为一个常见的理论假设失败了，即电子在原子晶体中的运动可以独立考虑。事实上，任何一个电子的运动都与所有其他电子的运动密切相关。PI和她的研究团队将结合联合收割机分析和数值方法来应对这一挑战。除了理论上的洞察力，该项目还可能导致利用这些强相关现象的技术应用。该奖项将使一系列教育和推广活动成为可能，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还将发起一个针对学前班和K-12学生及其家长的互动社区外展计划，旨在提高公众对量子物理和研究前沿的兴趣和欣赏。技术概述该职业奖支持在拓扑结构，相互作用和强相关相互作用中产生的巡游电子新量子现象的理论研究和教育。具体来说，PI将专注于开发新类别的多体拓扑状态的理论框架，并在强相关多轨道系统中的巡回铁磁性的非微扰方法。PI和她的团队将研究新的三维拓扑多体有序状态，其特征在于双调和对称性，包括超导和密度波状态。粒子-粒子（库珀）配对，或粒子-空穴配对，从费米表面拓扑继承了非平凡的Berry相位。它们的能隙函数不能在动量空间中全局定义，因此超出了基于球谐函数的旋转对称的标准实现。因此，无论特定的有序机制如何，它们都表现出拓扑保护的节结结构，并且只能用简谐函数来表征。巡回铁磁性是基于费米表面不稳定性而非局域自旋矩有序性的移动的电子的铁磁性。然而，它缺乏一个控制良好的弱耦合描述;轨道简并度和铁磁性机制之间的关系到目前为止还缺乏一个精确的答案，主要是由于缺乏处理强磁涨落的非微扰结果。PI和她的团队将开发非微扰方法，结合分析方法和无偏数值模拟，研究轨道简并在巡游铁磁性机制中的作用，以及巡游电子在铁磁性转变附近的强相关效应。该奖项将开展一系列教育和推广活动，从指导研究生，本科生和高中生，开发新的课程材料与研究项目，涵盖现代数学方法在凝聚态物理学的应用。PI还将发起一个针对学前班和K-12学生及其家长的互动社区外展计划，旨在提高公众对量子物理和研究前沿的兴趣和欣赏。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.