CAREER: New Platforms for Topology, Correlation, and Superconductivity in Quantum Materials

该职业奖支持强相关量子材料与物质拓扑相之间相互作用的理论研究和教育。强相关量子材料是一种固体，其中电子的行为是集体的，而不是单个粒子，而拓扑相表现出对噪声、缺陷和杂质不敏感的行为。在过去的几十年里，在这两个主题的推动下，凝聚态物理学取得了巨大的进步，从高温超导体到拓扑绝缘体和拓扑超导体。这些进步不仅加深了我们对多体系统量子物理的理解，而且具有巨大的革命性应用潜力，从商用核磁共振成型机和无损电力传输到不再是未来概念的量子计算机。虽然从历史上看，这两个研究领域在很大程度上是分开发展的，但近年来，越来越清楚的是，它们的协同作用揭示了更丰富的新现象和更大的应用潜力。一个突出的例子是所谓的云纹平带材料，包括最近发现的魔角扭曲双层石墨烯超导体。当两层石墨烯相互扭曲并改变电子密度时，该体系呈现出多种拓扑相和非常规超导相。虽然有很多潜在的应用，但形成这些相的基本机制仍在深入研究中。这些发展为拓扑和相关效应的交叉突破提供了令人兴奋的机会。PI将在多个方向上追求研究目标。PI将开发基于高阶拓扑相位概念的新拓扑量子计算平台所需的想法，高阶拓扑相位在体积和边缘上似乎没有特征，但在角落上承载非平凡状态。PI将揭示拓扑半金属中的各种拓扑超导相，为研究拓扑和相互作用效应提供了理想的平台。为了正确地解决强相关性的作用，PI将为量子多体系统开发新的理论和数值方法，这些方法不能被摄动理论捕获，并将这些方法应用于拓扑系统，包括电影平带。本项目所涉及的密切相关的研究课题将推动拓扑相位及其应用的前沿。该项目的一个组成部分是高中、本科和研究生阶段的教育计划，特别强调加强学术界和STEM劳动力的包容性和多样性。PI将参与佛罗里达大学现有的项目，通过讲座和对暑期研究项目的直接指导来接触高中生。PI将在物理系举办一系列研讨会，重点关注学术界内外的职业发展。通过调整和发展研究生水平的课程，PI将填补初级凝聚态物理学家培训的空白，通过连接传统主题和现代方面，如拓扑相。通过将推广和教育整合到研究计划中，这项工作将为不同背景的年轻公民提供独特的学习和研究经验，在量子物理及其潜在应用的前沿，确保被美国国家科学基金会确定为“未来投资十大理念”之一的基础“量子飞跃”的成功。本项目重点研究物质的拓扑相，特别是拓扑超导性和强相关系统之间的交集。在项目的第一部分，PI将基于拓扑绝缘体和拓扑有序态的拓扑缺陷特征，建立一个新的高阶拓扑相分类框架。PI将展示高阶拓扑超导作为编织非阿贝尔任意子的新平台的潜在应用。第二部分重点展示了相互作用的拓扑半金属作为新型拓扑相的天然宿主，包括高阶拓扑超导和具有Bogoliubov费米表面的超节点拓扑超导体。最后一部分致力于对承认拓扑超导不稳定性的理论模型进行仔细检查。这些模型涉及在量子临界点附近的低能费米子与软玻色子模式相互作用，从而引起非常规的超导不稳定性。为了进一步了解这些模型中的强相关性和丰富相位，PI将采用和开发量子蒙特卡罗方法和在大n极限下精确可解的sachdev - ye - kitaev类模型。从更广泛的角度来看，这些结果将把凝聚态物理学的两个蓬勃发展的领域联系起来：非常规超导和物质的拓扑相。结合这两个快速发展领域的工具和思想将极大地加深我们对量子多体物理的理解。该项目也有三个主要的教育组成部分，针对不同职业阶段的学生。PI将与佛罗里达大学大学预科教育和培训中心合作，通过量子计算基础知识的讲座和个人研究项目，积极吸引有动力的高中生。该教育计划的重点是加强学术界和STEM劳动力的包容性和多样性，其中包括一系列专注于物理专业学生和物理研究生职业发展的研讨会。通过专题和定期研究生课程的长期计划，PI将为量子多体物理开发一个新的教学框架，自然地结合这些系统的微扰，非微扰和拓扑方面，这更适合凝聚态物理的现代研究活动。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 on the interplay between strongly correlated quantum materials and topological phases of matter. Strongly correlated quantum materials are solids in which the electrons behave collectively rather than an individual particles, while topological phases exhibit behavior that is insensitive to noise, defects, and impurities. Over the past decades, driven by these two topics, condensed-matter physics has witnessed great progress, with examples ranging from high-temperature superconductors to topological insulators and topological superconductors. These advances not only deepened our understanding of the quantum physics of many-body systems but also hold enormous potential for revolutionary applications, from commercial MRI machines and lossless power transmission to quantum computers that are no longer a futuristic concept. While historically the two areas of research have, in large part, developed separately, in recently years it has become increasingly clear that their synergy reveals even richer novel phenomena and greater potential for applications. One prominent example is the so-called moire flat-band materials, including the recently discovered magic-angle twisted bilayer graphene superconductor. When two layers of graphene are twisted relative to each other and the electron density varied, the system exhibits a variety of topological phases and unconventional superconducting phases. While potential applications abound, the fundamental mechanism for forming these phases is still under intensive investigation. These developments present an exciting opportunity for breakthroughs at the intersection of topology and correlation effects.The PI will pursue the research goal in multiple directions. The PI will develop the ideas needed for a new topological quantum-computing platform based on the notion of higher-order topological phases, which seem featureless in the bulk and on the edge but host nontrivial states on the corners. The PI will uncover various kinds of topological superconducting phases in topological semimetals, which form an ideal playground for examining topology and interaction effects. To properly address the role of strong correlations, the PI will develop new theoretical and numerical approaches for quantum many-body systems that are not captured by perturbation theory and apply these approaches to topological systems, including morie flat bands. The closely related research topics addressed in this project will advance the forefronts of topological phases and their applications.An integral component of this project is an education plan at high-school, undergraduate and graduate levels, with a specific emphasis on enhancing inclusion and diversity in academia and the STEM workforce. The PI will participate in existing programs at the University of Florida to reach out to high school students through lectures and direct mentorship on summer research projects. The PI will host a series of seminars in the physics department that focuses on career development within and outside academia. Via adapting and developing graduate-level courses, the PI will fill a gap in the training of junior condensed-matter physicists by bridging traditional topics and modern aspects such as topological phases.By integrating outreach and education into the research plan, this work will provide young citizens of diverse backgrounds with unique learning and research experiences at the forefront of quantum physics and its potential applications, ensuring the success of the fundamental "Quantum Leap" identified by NSF as one of the "10 Big Ideas for Future Investment".TECHNICAL SUMMARYThis project focuses on the intersection between topological phases of matter, in particular topological superconductivity, and strongly correlated systems. In the first part of the project, the PI will establish a new classifying framework for higher-order topological phases based on characterization of topological defects in topological insulators and topological ordered states. The PI will demonstrate the potential application of higher-order topological superconductivity as a new platform for braiding non-Abelian anyons. The second part focuses on demonstrating interacting topological semimetals as natural hosts of novel topological phases, including higher-order topological superconductivity and ultra-nodal topological superconductors with Bogoliubov Fermi surfaces. The final part is devoted to a close examination of theoretical models that admit topological superconducting instabilities. These models involve low-energy fermions in the vicinity of a quantum-critical point interacting with soft bosonic modes, which induce unconventional superconducting instabilities. To further understand the strong correlation and rich phases in these models, the PI will adopt and develop Quantum Monte Carlo methods and a Sachdev-Ye-Kitaev-like model that is exactly solvable in a large-N limit. In broader terms, these results will connect two thriving fields of condensed matter physics: unconventional superconductivity and topological phases of matter. Combining tools and ideas from both rapidly developing fields will tremendously deepen our understanding of quantum many-body physics.The project also has three main educational components targeting students at different career stages. In collaboration with the University of Florida's Center for Precollegiate Education and Training, the PI will actively engage motivated high-school students through lectures on the basics of quantum computing and through individual research projects. With an emphasis on enhancing inclusion and diversity in academia and the STEM workforce, the education plan includes a series of seminars focused on career development for physics majors and physics graduate students. Through a long-term plan of special-topic and regular graduate courses, the PI will develop a new pedagogical framework for quantum many-body physics that naturally incorporates perturbative, non-perturbative, and topological aspects of these systems, which better suits modern research activities in condensed-matter physics.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.