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

该职业奖支持快速发展的材料物理学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特性和表现现象，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种材料的一个特别突出的例子，拓扑材料。拓扑材料的强健电子特性可以借助从几何和形状研究中衍生出来的抽象数学概念来理解。当这些材料中的电子强烈相互作用时，就会发生令人惊讶的奇特现象。理解这些现象和支配它们的基本原理是迈向新能源和计算技术的关键一步。该项目的目标是为描述和理解这种强相互作用材料提供一个新的范例，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，该工作介绍了一种描述相互作用电子系统的形式，该系统超出了当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性质和行为的新见解的大门，特别是奇异量子态的性质，并用于识别这些实现的材料。该项目将系统地发展和扩展所提出的形式主义，重点关注具有不同结构、化学和对称性质的二维和三维系统和材料。概念上的进步将为材料预测和发现提供新的途径，目的是在相关拓扑量子态的前沿实现实验进展。量子材料似乎是下一代技术创新的中心，同时也为物质的基本组成部分提供了独特的见解。该奖项还支持旨在提高量子材料研究可见度和扩大凝聚态物理参与的教育和推广领域的活动。这些活动有助于量子材料和技术的劳动力。支持的举措包括：(i)建立一个对非物理学家开放的量子技术专业发展证书课程，（ii）启动一个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预科研究机会，以及（iv）通过本科生外展计划扩大凝聚态物理学的范围和知名度。该职业奖支持快速发展的量子材料领域的理论研究和教育，特别关注强相关拓扑量子材料。拓扑材料是一类新的量子材料，它揭示了抽象数学概念（例如波函数的拓扑）和物理材料特性（例如固有鲁棒传输通道的存在）之间的深刻联系。我们对拓扑材料的理解依赖于现代固体能带理论的中心支柱之一：能带反转的概念。鉴于其在推进我们对金属和绝缘体的认识方面取得的显著成功，该项目的目标是将能带反转范式推广到强相互作用的拓扑量子态。这种多体带反转范式提供了一种基于波函数的方法来研究量子材料中强相关拓扑量子相的结构、性质和功能。它克服了量子霍尔效应激发的平带范式固有的局限性，为识别可能实现奇异相关量子态的材料提供了新的材料视角。研究活动分为三个相互关联和互补的研究重点。第一个重点将放在二维系统上。计算方法将用于绘制模型系统中接近相关带反转过渡的真实材料的相图。此外，现有的相关拓扑半金属的实验工作将进行审查。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，并提出了将多体带反转推广到三维的途径。第三个逆冲是在前两个逆冲的基础上提出的，并提出了一个在带反转跃迁中实现强相关拓扑基态的材料平台。这些推力推进了在当前范式之外发现新的相关拓扑阶段的共同目标。该奖项还支持教育和外展领域的活动。这些活动与拟议的研究紧密结合，并利用量子材料的优势作为未来技术的关键资源。支持的举措包括：(i)建立一个对非物理学家开放的量子技术专业发展证书课程，（ii）启动一个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预科研究机会，以及（iv）通过本科生外展计划扩大凝聚态物理学的范围和知名度。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 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.