CAREER: Advancing the Many-body Band Inversion Paradigm for Correlated Quantum Materials

非技术总结这个职业奖项支持快速发展的材料物理领域的理论研究和教育，即量子材料。量子材料具有深深植根于量子物理定律的性质和现象，从而为未来的量子技术提供了关键资源。这个项目特别关注这类材料的一个特别突出的例子--拓扑材料。借助几何和形状研究中的抽象数学概念，可以理解拓扑材料非常强健的电学性质。当这些材料中的电子相互作用强烈时，可能会发生令人惊讶的奇异现象。了解这些现象和管理它们的基本原则是迈向新能源和计算技术的关键一步。这个项目的目标是提出一种新的范式来描述和理解这种强相互作用的材料，从而为材料发现提供一个新的视角。研究活动将建立在PI最近的工作基础上，它引入了一种形式主义来描述相互作用电子系统，这些电子系统不属于目前理解强相互作用的主要范式。这种形式主义打开了对物质基本属性和行为的新洞察之门，特别是奇异量子态的属性，并用于识别实现这些属性的材料。这个项目将系统地发展和扩展所提出的形式主义，专注于具有不同结构、化学和对称性质的二维和三维的系统和材料。概念上的进展将为材料预测和发现提供新的途径，目的是使相关拓扑量子态的前沿实验能够取得进展。量子材料似乎处于下一代技术创新的中心，同时为物质的基本组成部分提供了独特的见解。该奖项还支持教育和推广领域的活动，旨在提高量子材料研究的可见度，扩大对凝聚态物理的参与。这些活动有助于量子材料和技术方面的劳动力。所支持的计划包括：(I)建立面向非物理学家的量子技术专业发展证书计划；(Ii)开办内部量子材料暑期学校，作为合作孵化器；(Iii)提供多样化和包容性的研究生前研究机会；以及(Iv)通过本科生外展计划扩大凝聚态物理的影响范围和能见度。TECHNICAL SUMMARY该职业奖项支持快速发展的量子材料领域的理论研究和教育，特别是强关联量子拓扑材料。拓扑材料是一类新的量子材料，它揭示了抽象的数学概念之间的深刻联系，例如波函数的拓扑，与物理材料性质之间的关系，例如本质上强健的传输通道的存在。我们对拓扑材料的理解依赖于现代固体带理论的核心支柱之一：带反转的概念。鉴于它在提高我们对金属和绝缘体的知识方面取得的巨大成功，这个项目的目标是将带反转范例推广到强相互作用的拓扑量子态。这种多体能带反转模式提供了一种基于波函数的方法来研究量子材料中强关联拓扑量子相的结构、性质和功能。它克服了受量子霍尔效应启发的平带范式所固有的局限性，为识别可能实现奇异关联量子态的材料提供了新的材料视角。研究活动被组织在三个相互关联和互补的研究推力中。第一个推力将集中在两个维度的系统上。计算方法将被用来绘制在关联带反转转变附近的真实材料的模型系统中的相图。此外，还将考察相关拓扑半集的现有实验工作。第二个推力涉及三维系统，特别是具有较高角动量的带反转拓扑半金属，并提供了一条将多体能带反转推广到三维的途径。第三个推力来自于前两个推力的洞察，并提出了在能带反转跃迁中实现强关联拓扑基态的材料平台。这些努力推进了共同的目标，即发现当前范例之外的新的相关拓扑阶段。该奖项还支持教育和外联领域的活动。这些活动与拟议的研究紧密结合在一起，并利用量子材料作为未来技术的关键资源的优势。支持的举措包括：(I)建立面向非物理学家的量子技术专业发展证书计划，(Ii)推出内部量子材料暑期学校作为合作孵化器(Iii)，提供多样化和包容性的研究生前研究机会，以及(Iv)通过面向本科生的外联计划扩大凝聚态物理的覆盖范围和能见度。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 CAREER award supports theoretical research and education in the rapidly developing field of materials physics known as quantum materials. Quantum materials have properties and exhibit phenomena deeply rooted in the laws of quantum physics, thus providing a key resource for future quantum-based technologies. This project specifically focuses on a particularly prominent example of such materials, the topological materials. The remarkably robust electronic properties of topological materials can be understood with the help of abstract mathematical concepts derived from the study of geometry and shape. When the electrons in these materials are strongly interacting, surprising and exotic phenomena can occur. Understanding these phenomena and the fundamental principles that govern them is a key step towards new energy and computing technologies. The goal of this project is to advance a new paradigm for describing and understanding such strongly interacting materials, and thereby to provide a new perspective for materials discovery.The research activities will build on recent work of the PI, which introduced a formalism for describing systems of interacting electrons that fall outside the currently predominant paradigm for understanding strong interactions. This formalism opens the door to new insight into fundamental properties and behavior of matter, in particular the properties of exotic quantum states, and serves to identify materials in which these are realized. This project will systematically develop and extend the proposed formalism, focusing on systems and materials in two and three dimensions with different structure, chemistry, and symmetry properties. Conceptual advances will be leveraged to provide new pathways to materials prediction and discovery, with the aim of enabling experimental progress on the frontier of correlated topological quantum states.Quantum materials appear to be at the epicenter of next-generation technological innovation, while at the same time offering unique insight into the fundamental building blocks of matter. This award also supports activities in the areas of education and outreach designed to increase the visibility of quantum materials research and to broaden participation in condensed matter physics. These activities contribute to the workforce in quantum materials and technologies. Supported initiatives include: (i) building a professional development certificate program in quantum technology open to non-physicists, (ii), launching an in-house quantum materials summer school as incubator for collaboration (iii), offering diverse and inclusive pre-graduate research opportunities and (iv) expanding the reach and visibility of condensed matter physics through an outreach program for undergraduates.TECHNICAL SUMMARYThis CAREER award supports theoretical research and education in the rapidly developing field of quantum materials, with a specific focus on strongly correlated topological quantum materials. Topological materials are a new class of quantum materials which have exposed a deep connection between abstract mathematical concepts, for example the topology of wave functions, and physical material properties, for example the presence of intrinsically robust transport channels. Our understanding of topological materials relies on one of the central pillars of the modern band theory of solids: the notion of a band inversion. Given its remarkable success in advancing our knowledge of metals and insulators, the goal of this project is to develop a generalization of the band inversion paradigm to strongly interacting topological quantum states. This many-body band inversion paradigm offers a wave function-based approach to studying the structure, properties, and function of strongly correlated topological quantum phases in quantum materials. It overcomes limitations inherent in the flat-band paradigm inspired by the quantum Hall effect and offers a new materials perspective for identifying materials which may realize exotic correlated quantum states.The research activities are organized in three interrelated and complementary research thrusts. The first thrust will focus on systems in two dimensions. Computational methods will be employed to map out the phase diagram in model systems for real materials near a correlated band inversion transition. In addition, existing experimental work on correlated topological semimetals will be examined. The second thrust is concerned with systems in three dimension, in particular band-inverted topological semimetals with higher angular momentum and presents a pathway to generalizing the many-body band inversion to three dimensions. The third thrust is informed by the insight of the first two thrusts and suggests a materials platform for realizing strongly correlated topological ground states at a band inversion transition. These thrusts advance the common goal of uncovering new correlated topological phases outside of the current paradigm.This award also supports activities in the areas of education and outreach. These activities are tightly integrated with the proposed research and harness the ascendance of quantum materials as a key resource for future technology. Supported initiatives include: (i) building a professional development certificate program in quantum technology open to non-physicists, (ii), launching an in-house quantum materials summer school as incubator for collaboration (iii), offering diverse and inclusive pre-graduate research opportunities and (iv) expanding the reach and visibility of condensed matter physics through an outreach program for undergraduates.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.