CAREER: Interplay of topology and geometry in materials with strong spin-orbit coupling

这项由材料研究部资助的职业资助金旨在改变我们对电子系统中自旋-轨道耦合和粘弹性输运之间关系的理解。具有强自旋-轨道耦合的材料对局部轨道取向的敏感性要求对传统的粘弹性响应理论进行改革，并为尚未发现的普遍和量子化的拓扑输运现象留下了可能性。提出的理论借鉴了高能物理和引力的想法，这些想法适用于凝聚态物质，然后用于预测真实材料中的现象，并解决了高能界关于扭转在手性反常中的作用的争议，手性反常只能通过凝聚态物质的洞察来解决。这些发展应用的材料集是广泛的、可通过实验获得的，并且处于现代研究活动的前沿。包括：拓扑绝缘体、拓扑Weyl半金属和自旋轨道耦合半导体异质结/量子线。利用量子和半经典技术，将分析这些材料中的粘弹性输运，以识别新的现象并预测输运系数的值。首先要研究的标志性现象是在二维时间反转击穿拓扑绝缘子中发现的无耗散拓扑粘性。随着对现实材料的研究，关于拓扑输运、弹性变形几何和量子场论之间的关系，还有一些深层次的概念性问题需要解决。非技术综述凝聚态物理学的主要目标之一是找到复杂系统的普遍性质，即与真实材料中固有的复杂细节无关的性质。值得注意的是，材料的所谓拓扑电子性质对细节非常不敏感，即使使用粗略的模型，也可以精确地定量预测它们。事实上，拓扑性质是如此非凡，以至于在20世纪80年代初首次发现量子化霍尔电导率，导致了两次诺贝尔奖和测量，它们是如此准确，以至于它们现在成为电阻单位的国际标准。在过去的10年里，人们从理论上预测和实验上发现了许多新的物质相族，它们每一类都表现出特殊的拓扑性质。虽然大部分注意力都集中在这些材料对纯粹的电磁探测器的反应上，但这份职业提案试图了解这些系统如何对形状的本质变化做出反应。与拓扑学领域不同，几何学对长度和形状的精确定义感兴趣，因此是在广泛的拓扑特征之上的额外的细节层次。然而，在这些材料中，拓扑电子性质和材料的几何形状之间存在着重要的相互作用。令人兴奋的是，即使当我们考虑依赖于细节的几何探测时，结果也可能最终是一个健壮的拓扑属性。因此，当几何学和拓扑学竞争时，有时拓扑学仍然可以获胜。这些发展所应用的材料集是广泛的、可通过实验获得的，并且处于现代研究活动的前沿。这里研究的拓扑量是一种尚未开发的资源，它肯定会导致量子现象，这些现象可以被整合到独特的设备中。这种技术影响，再加上在这一研究领域中高能物理、引力和凝聚态之间发展起来的有价值的思想交流，表明了这笔赠款的广泛性。此外，这一职业致力于将本科生融入前沿研究，并培训本科生、研究生和博士后研究人员的沟通和研究技能，这将有利于他们未来的职业生涯。

Technical SummaryThis CAREER grant, supported by the Division of Materials Research, aims to transform our understanding of the relationship between spin-orbit coupling and visco-elastic transport in electron systems. The sensitivity of materials with strong spin-orbit coupling to local orbital orientation requires a reformation of the conventional visco-elastic response theories, and leaves open the possibility for undiscovered topological transport phenomena that are universal and quantized. The proposed theory draws on ideas from high-energy physics and gravitation that are adapted to condensed matter and then used to predict phenomena in real materials, and to resolve a controversy in the high-energy community on the role of torsion in the chiral anomaly that will only be solved with condensed matter insight.The set of materials to which these developments apply is broad, experimentally accessible, and at the forefront of modern research activity. The set includes: topological insulators, topological Weyl semi-metals, and spin-orbit coupled semiconductor heterostructures/quantum wires. Using quantum and semi-classical techniques, the visco-elastic transport in these materials will be analyzed to identify new phenomena and to predict the values of the transport coefficients. The landmark phenomenon that will be studied first is the dissipationless topological viscosity found in 2d time-reversal breaking topological insulators. Along with the study of realistic materials, there are deep conceptual issues that will be resolved regarding the relationship between topological transport, the geometry of elastic deformations, and quantum field theory. Non-Technical SummaryOne of the key goals of condensed matter physics is to find properties of complex systems that are universal, i.e., properties that are independent of the complicated details inherent in real materials. Remarkably, the so-called topological electronic properties of a material are so insensitive to details that they can be quantitatively predicted to exquisite precision even when crude models are employed. In fact, topological properties are so remarkable that the first discovery of one in the early 1980s, the quantized Hall conductivity, led to two Nobel prizes and measurements that were so accurate that they now serve as the SI standard for units of resistance. In the past 10 years many new families of phases of matter which each exhibit special types of topological properties have been theoretically predicted and experimentally discovered. While most of the focus has been on how these materials respond to purely electromagnetic probes, this CAREER proposal seeks to understand how these systems respond to essentially changes of shape. Unlike the field of topology, geometry is interested in precise definitions of lengths and shapes, and thus is an extra level of detail on top of the broad topological features. However, in these materials there is an important interplay between the topological electronic properties and the geometry of the material. The exciting thing is that even when we consider detail-dependent geometrical probes, the outcome can end up being a robust topological property. Thus, when geometry and topology compete, sometimes topology can still win. The set of materials to which these developments apply is broad, experimentally accessible, and at the forefront of modern research activity. The topological quantities studied here are an untapped resource that is sure to lead to quantum phenomena that can be incorporated into unique devices. This technological impact, coupled with the valuable interchange of ideas, developed during this line of research, between the fields of high-energy physics, gravitation, and condensed matter indicate the broadness of this grant. In addition, this CAREER is dedicated to the integration of undergraduates into cutting-edge research, and the training of undergraduates, graduate students, and postdoctoral researchers in communication and research skills that will benefit their future careers.