Theories of Transport and Optical Phenomena in Topological and Correlated Materials

该奖项支持研究和教育，以了解材料的基本电子和光学特性。材料的电子和光学性质构成了许多现代信息技术的基础。新发现的材料被归类为“拓扑材料”，它们以独特的方式对施加的电场和磁场做出反应，在某些情况下，它们的特性对杂质的影响可能异常强大。该项目研究部分的第一个领域涉及开发理论方法来预测和理解拓扑材料的性质，扩展了该领域以前的工作。一个特别的重点是提高我们对材料用强激光研究时出现的光学性质的理解。这些材料中的电子实际上是无质量的，这为基础科学和技术创造了令人兴奋的机会。另一个主要的研究领域是了解在一个非常干净的材料中电子之间的相互作用如何导致电子的流体般的集体运动，但与正常流体（如水）的流动相比有有趣的差异。了解这些流体动力学流动的电子，或原子气体中的原子，可以帮助设计未来几代的电子设备。在这个项目的教育工作包括几个活动超出标准的专业课堂教学和指导研究生。PI正在编写一本教科书，这将是一个广泛的介绍拓扑材料，建立在他以前出版的讲义。他将与当地科学教师和公众开展外联活动，让他们了解量子材料的最新发展。本科生将参与介绍性的研究问题，让他们对上述领域的现代研究有一种感觉。技术总结本项目将量子凝聚态物理学两个领域的研究与相关的教育和推广活动相结合。 研究的一个领域是关于电子的无间隙拓扑状态，建立在新材料和新现象的发现之上。另一个领域涉及相互作用的电子金属中的传输，包括在非常干净的材料中出现的流体动力学效应。这项工作的主要影响是教育，主要是PI的研究生，但也包括科学家和非科学家，以及理解未来量子技术的物理基础。PI试图理解量子凝聚态物理学两个领域中的新型电子行为。一个领域涉及金属或无间隙材料的拓扑行为。两个最近发现的例子与历史悠久的理论可能性是拓扑大块半金属的外尔或狄拉克型。这些以及更复杂的状态，如无隙自旋液体，是活跃的实验和理论研究的主题，但与绝缘情况相比，它们可能具有什么独特的性质还没有很好的理解。这一研究方向建立在最近关于非线性光学和其他通常不被认为具有拓扑起源的性质如何在拓扑阶段变得意想不到的强大甚至量子化的有希望的结果的基础上。支持的工作将推进对这类材料更系统的理解，包括相互作用效应，并找到超越线性响应的拓扑行为的新例子。简单流体的流体力学可以说是相互作用凝聚态系统的第一个简化或“有效”理论。第二个研究领域涉及电子长时间、长距离动力学中产生的流体动力学的修改形式与传统经典流体动力学的不同之处，传统经典流体动力学描述了像普通水这样的简单流体。近年来的理论工作已经给出了几个例子，说明材料中的电子流体力学如何不同于普通的经典单组分流体力学，无论是从额外的守恒量，库仑排斥的长程性质，还是打破对称性，如时间反转或反转。量子流体的行为在实验上非常重要，对于由非常干净的材料制成的小长度尺度的实际设备中的实际传输，并且与关于热化和弛豫速率的深层次问题有关。教育活动包括本科生和研究生监督和课堂教学，在高等学校讲课以及共同撰写拓扑物质的入门教科书，以及对学校和教师的宣传。该教育工作的一个目标是将量子凝聚态物理学最新发现的魔力带给更广泛的受众。该奖项反映了NSF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 award supports research and education towards understanding fundamental electronic and optical properties of materials. The electronic and optical properties of materials form the basis of much of modern information technology. Newly discovered materials that go under the classification "topological materials" respond in unique ways to applied electric and magnetic fields, and their properties in some cases can be unusually robust to impurities. The first area of the research portion of this project involves developing theoretical methods to predict and understand properties of topological materials, extending previous work in this area. A particular focus is on improving our understanding of the optical properties that appear when materials are studied with intense laser light. The electrons in these materials appear effectively massless, which creates exciting opportunities for basic science and technology.The other main area of research involves understanding how interactions between electrons in a very clean material lead to fluid-like collective motion of electrons, but with interesting differences compared to the flow of a normal fluid, like water. Understanding these hydrodynamical flows of electrons, or of atoms in an atomic gas, could help in the design of future generations of electronic devices.Educational work in this project includes several activities beyond standard professorial classroom teaching and mentoring of graduate students. The PI is working on a textbook that will be a broad introduction to topological materials, building on his previously published lecture notes. He will pursue outreach activities with local science teachers and with the general public, to give them a sense of recent developments in quantum materials. Undergraduates will be involved in introductory research problems to give them a sense of modern research in the above areas.TECHNICAL SUMMARYThis project combines research in two areas of quantum condensed matter physics with related education and outreach activities. One area of research is concerned with gapless topological states of electrons, building on discoveries of new classes of materials and new phenomena that they enable. The other area involves transport in interacting electron metals including hydrodynamic effects that arise in very clean materials. The main broader impacts of the work to be conducted are on education, primarily of the PI's graduate students but also of scientists and non-scientists more generally, and on understanding the physical underpinnings of future quantum technologies.The PI seeks to understand new kinds of electronic behavior in two areas of quantum condensed matter physics. One area involves topological behavior in metallic or gapless materials. Two recently discovered examples with a long history as theoretical possibilities are the topological bulk semimetals of Weyl or Dirac type. These, and more complicated states such as gapless spin liquids, are subjects of active experimental and theoretical study, but what unique properties they might have is not well understood, compared to the insulating case. This research direction builds on promising recent results on how nonlinear optics and other properties not usually thought of as having a topological origin can become unexpectedly strong and even quantized in topological phases. The supported work will advance the understanding of these kinds of materials more systematically, including interaction effects, and find new examples of topological behavior beyond linear response.Hydrodynamics of simple fluids was arguably the first simplified or "effective" theory of an interacting condensed matter system. The second area of research involves how the modified forms of hydrodynamics arising in the long-time, long-distance dynamics of electrons differ from conventional classical hydrodynamics, which describes a simple fluid like ordinary water. Theoretical work in recent years has given several examples of how electron hydrodynamics in materials can differ from ordinary classical single-component hydrodynamics, whether from extra conserved quantities, the long-ranged nature of Coulomb repulsion, or broken symmetries such as time-reversal or inversion. The behavior of quantum fluids is both experimentally important, for actual transport in practical devices made from very clean materials at small length scales, and is connected to deep questions about thermalization and relaxation rates.Educational activities include undergraduate and graduate student supervision and classroom teaching, lecturing at advanced schools and co-authorship of an introductory textbook on topological matter, and outreach to schools and teachers. One goal of the educational work is to bring some of the magic of recent discoveries in quantum condensed matter physics to a broader audience.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.