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.

非技术总结该职业奖支持量子材料快速发展的领域的研究和教育。量子材料是指电子的集体行为产生非凡的特性，并在量子技术中具有潜在应用，从旋转技术到量子计算。在范式转移发现的范式中，数学领域描述了物体变形时保持不变的特性，可以识别出出色的材料，例如内部内部的绝缘剂，但在其表面和拓扑中存在的状态和边缘上通过状态和边缘进行了潜在的无耗电电力传导的材料。拓扑在确定每种材料中发现哪些电子物质阶段以及它们可能是物质的外来电子状态后可能是长期散布的电子物质的可能性。示例是超导性，其中电子在整个材料或阶段的流动完全零，在这些材料或相位中，电子似乎将电子分离为具有非常规性能的较小实体，称为分数阶段。PI将研究拓扑结构和量子几何形状，即量子状态的抽象代表的几何特性如何影响电子的本质，尤其是在材料中呈现出不可或缺的材料。仔细控制缺陷可以实现具有所需特性的电子物质阶段。通过这项研究，PI旨在深入了解独特的量子现象的稳定性，并为拓扑量子材料的表征以及预测和进行实验，发现新项目的发现，为研究和教育提供了多种努力，这些努力集中在量化量的研究生上，为研究和多样化而集成了他们的量化培训。该活动将包括一个训练营涵盖拓扑材料的必需品和用于研究其电子特性的计算技术。 PI还将组织一个研讨会，展示来自从事量子材料的潜水员背景的才华横溢的年轻研究人员。技术摘要这一职业奖支持理论研究和教育，旨在研究量子几何形状在固态电子产品集体特性中的影响。 PI将探索电子波函数的动量空间纹理如何影响清洁和肮脏材料中的电子行为，影响远距离连贯性，运输以及外来兴奋的出现。该项目侧重于对量子材料的新观点，目的是从绿色功能运算符结构的角度统一量子几何现象，尤其是当将其投影到各种空间缺陷时，其拓扑具有稳健的零。这种方法的目的是构建可以有效地应用的工具，以识别有或没有翻译对称性的系统中的非平凡几何形状，因此为1）开放了可能性，以表征无序的拓扑结晶物的行为； 2）提供搜索具有特色卓越的新材料的准则； 3）确定源于基态的非平凡几何形状的强大身体反应。这种方法将对拓扑问题的毛刺领域产生显着贡献，并在电子结构理论，化学和材料科学中应用。该活动还包括建立一个训练营，以计算材料拓扑特性，涵盖频段理论，群体理论和密度功能理论的基本要素，并允许学生获得模拟各种实验和技术相关性的“动手”经验。 PI还旨在建立一个基于纽约市的研讨会，以关注来自潜水员背景的优秀年轻研究人员。该奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响评估标准来评估，被认为是珍贵的支持。