Theories of Transport and Optical Phenomena in Topological and Correlated Materials

非技术总结该奖项支持了解材料的基本电学和光学性质的研究和教育。材料的电子和光学特性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外加电场和磁场做出反应，在某些情况下，它们的性质对杂质可能会异常坚固。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，扩展了以前在这一领域的工作。一个特别的重点是提高我们对用强激光研究材料时出现的光学性质的理解。这些材料中的电子似乎实际上是无质量的，这为基础科学和技术创造了令人兴奋的机会。另一个主要研究领域涉及了解非常干净的材料中电子之间的相互作用如何导致电子像流体一样的集体运动，但与正常流体(如水)的流动相比，有有趣的区别。了解这些电子或原子气体中的流体力学流动，有助于设计未来一代的电子设备。这个项目的教育工作包括几个超出标准的教授课堂教学和研究生辅导的活动。PI正在编写一本教科书，这本教科书将在他之前出版的讲稿的基础上，广泛介绍拓扑材料。他将与当地科学教师和普通公众开展外联活动，让他们了解量子材料的最新发展。本科生将参与入门研究问题，使他们对上述领域的现代研究有一种感觉。技术总结这个项目将量子凝聚态物理两个领域的研究与相关的教育和推广活动结合在一起。一个研究领域涉及电子的无缝隙拓扑态，建立在新材料类别和它们实现的新现象的发现基础上。另一个领域涉及相互作用的电子金属的传输，包括在非常干净的材料中产生的流体动力学效应。将进行的工作的主要更广泛的影响是对教育，主要是国际和平研究所的研究生，但也包括更广泛的科学家和非科学家，以及了解未来量子技术的物理基础。国际和平研究所试图了解量子凝聚态物理的两个领域的新类型的电子行为。其中一个领域涉及金属或无间隙材料的拓扑行为。最近发现的两个具有理论可能性的例子是Weyl或Dirac类型的拓扑体半金属。这些状态，以及更复杂的状态，如无间隙自旋液体，都是积极的实验和理论研究的主题，但与绝缘情况相比，它们可能具有哪些独特的性质还不是很清楚。这一研究方向建立在令人振奋的最新结果基础上，即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变得出人意料地强大，甚至在拓扑阶段被量子化。所支持的工作将更系统地推进对这类材料的理解，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。简单流体的流体动力学可以说是第一个简化或“有效”的相互作用凝聚态系统的理论。第二个研究领域涉及在电子的长时间、远距离动力学中出现的改进形式的流体力学与传统的经典流体力学有何不同，传统的经典流体力学描述的是像普通水一样的简单流体。最近几年的理论工作给出了几个例子，说明材料中的电子流体动力学如何不同于普通的经典单分量流体动力学，无论是从额外的守恒量、库仑排斥的长程性质，还是对称的破坏，如时间反转或反转。量子流体的行为不仅在实验上很重要，对于在由非常干净的材料制成的实际设备中的实际传输来说，长度很小，而且与关于热化和驰豫速率的深层次问题有关。教育活动包括本科生和研究生的监督和课堂教学，在高等学校的讲课和与人合著一本关于拓扑物质的入门教科书，以及接触学校和教师。教育工作的一个目标是将量子凝聚态物理学最新发现的一些魔力带给更广泛的受众。这一奖项反映了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 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.