CAREER: Geometry and topology of quantum materials

职业：量子材料的几何和拓扑

• 批准号: 2340394
• 负责人: Raquel Queiroz
• 金额: $ 60万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-05-01 至 2029-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2340394&HistoricalAwards=false
• 关键词: CAREER; Geometry; topology; quantum; materials

NONTECHNICAL SUMMARY This CAREER award supports research and education in the rapidly evolving field of quantum materials. Quantum materials refer to those in which the collective behavior of electrons gives rise to extraordinary properties with potential applications in quantum technologies from spintronics to quantum computing. In a paradigm shifting discovery, topology, the field in mathematics that describes properties which remain unchanged when objects are deformed, was recognized to result in remarkable materials such as those that are insulators in the interior but possess dissipationless electric conduction through states on their surfaces and edges that are required to exist by topology. Less explored but equally remarkable is the crucial role that topology plays in determining which phases of electronic matter are found in each material, and the possibility they might be long sought-after exotic electronic states of matter. Examples are superconductivity where electrons flow with exactly zero resistance in the entire material or phases where electrons seem to dissociate into smaller entities with unconventional properties, called fractionalized phases.The PI will study how topology and quantum geometry, the geometric properties of an abstract representation of quantum states, can influence the nature of electrons in matter, particularly when unavoidable imperfections or “dirt” are present in materials. Careful control of defects may enable phases of electronic matter with desired properties to be realized. Through this research, the PI aims to gain insights into the stability of unique quantum phenomena, as well as offer new mathematical tools for the characterization of topological quantum materials and for the prediction and, working with experiment, the discovery of new ones.In this project, research and education are integrated through multiple efforts focusing on graduate students that will enhance and diversify their training in quantum properties of matter. The activity will include a bootcamp covering essentials of topological materials and computational techniques for studying their electronic properties. The PI will also organize a workshop to showcase talented young researchers from diverse backgrounds working on quantum materials. TECHNICAL SUMMARYThis CAREER award supports theoretical research and education aimed to study the influence of quantum geometry in the collective properties of electrons in the solid state. The PI will explore how the momentum space textures of electron wavefunctions affect electron behavior in both clean and dirty materials, influencing long-range coherence, transport, and the emergence of exotic excitations. The project focuses on a new perspective on quantum materials, with the aim to unify quantum geometric phenomena from the point of view of the structure of the Green’s function operator, in particular its topologically robust zeros when projected to various spatial defects. The goal of this approach is to construct tools that can be efficiently applied to identify nontrivial geometry both in systems with and without translational symmetry, therefore opening the possibility to 1) characterize the behavior of disordered topological crystalline matter; 2) offer guidelines for the search of new materials with exceptional physical properties; 3) identify robust physical responses that stem from the nontrivial geometry of the ground state. This approach is set to contribute significantly to the burgeoning field of topological matter, with applications in electronic structure theory, chemistry, and materials science. This activity also includes establishing a bootcamp for the computation of materials topological properties covering the essentials of band theory, group theory, and density functional theory, and allowing students to gain "hands-on" experience simulating various quantities of experimental and technological relevance. The PI also aims to establish a New York City based workshop to spotlight excellent young researchers from diverse backgrounds.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.

非技术摘要 该职业奖支持快速发展的量子材料领域的研究和教育。量子材料是指电子的集体行为产生非凡特性，并在从自旋电子学到量子计算的量子技术中具有潜在应用的范例。拓扑学这一数学领域描述了物体变形时保持不变的特性，这一发现的转变被认为产生了非凡的材料，例如那些内部是绝缘体但具有无耗散导电的材料通过拓扑所需存在的表面和边缘上的状态，拓扑在确定每种材料中存在电子物质的相以及它们可能长期受到追捧的可能性方面发挥着至关重要的作用，这一点较少被探索，但同样引人注目。例子是超导性，其中电子在整个材料或相中以完全零的电阻流动，其中电子似乎解离成具有非常规特性的较小实体，称为分数化相。PI将研究拓扑和量子几何、几何特性量子态的抽象表示，可以影响物质中电子的性质，特别是当材料中存在不可避免的缺陷或“污垢”时，通过这项研究可以实现具有所需特性的电子物质的相。 PI 旨在深入了解独特量子现象的稳定性，并为拓扑量子材料的表征、预测以及通过实验发现新材料提供新的数学工具。多方努力，与教育融为一体该活动将包括一个涵盖拓扑材料和研究其电子特性的计算技术要点的训练营，以展示来自不同领域的才华横溢的年轻研究人员。技术摘要该职业奖支持旨在研究量子几何对固态电子集体特性的影响的理论研究和教育。PI 将探索电子波函数的动量空间纹理如何影响。该项目侧重于量子材料的新视角，旨在从量子的角度统一量子几何现象。格林函数算子的结构，特别是投影到各种缺陷时的拓扑鲁棒空间零点，该方法的目标是构建可以有效地应用于识别具有或不具有平移对称性的系统中的非平凡几何的工具，从而打开的可能性1）表征无序拓扑晶体物质的行为；2）为寻找具有特殊物理性质的新材料提供指导；3）识别源自基态的非平凡几何形状的强大物理响应。这项活动还包括建立一个涵盖能带理论、群论和密度泛函理论基础知识的材料拓扑特性计算训练营。并允许该项目旨在帮助学生获得模拟各种实验和技术相关性的“实践”经验。该项目还旨在建立一个位于纽约的研讨会，以吸引来自不同背景的优秀年轻研究人员。该奖项反映了 NSF 的法定使命，并被认为是值得的。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来获得支持。