THz Magneto-Optical Study of Topological Invariants in Dirac Materials and the GaAs 2DEG

****技术摘要****这个程序通过测量几个凝聚态系统在太赫兹频率下的磁光响应来解决拓扑不变量的物理问题。其中包括砷化镓异质结构和石墨烯中的交流量子霍尔效应，以及拓扑绝缘体中预测的量子化法拉第旋转。拓扑绝缘体是一种被预测的新型物质量子态，有望具有奇异的特性，包括拓扑保护的自旋极化导电表面态、本征磁电效应和由超导体邻近效应引起的马约拉纳费米子。石墨烯和拓扑绝缘体都在电子器件小型化、多功能传感器和数据存储应用、能量存储、自旋电子学和量子计算方面提供了潜在的创新。所有这些系统的霍尔量子化仅在零频率时受到拓扑保护。实验将研究这些拓扑不变量的频率分解，这对我们理解这些重要的基本约束是很重要的。PI开发了独特的太赫兹偏振调制技术，可以以前所未有的灵敏度测量法拉第和克尔旋转以及圆二色性。该项目还包括开发一套系统的教育光学实验室演示和教程，供马里兰大学和整个社区的本科生使用。****非技术摘要****拓扑学是研究光滑变形下不变物体性质的数学分支，甜甜圈变成咖啡杯就是一个经典的例子。在对称的情况下，拓扑学对物理系统的行为有着深刻的影响。因此，量子霍尔效应中霍尔电导率量子化的极端精度是二维电子系统边缘量子化电子态拓扑结构的结果。这种效应是电阻标准的基础。类似的拓扑效应导致某些绝缘体存在导电金属边界。拓扑不变量“保护”这些金属边界，使其成为良导体，对缺陷和无序不敏感。这些拓扑绝缘体是一种预测的新的物质量子态，最近因其预测的奇异性质而引起了人们的广泛关注。然而，拓扑绝缘体和量子霍尔系统中的拓扑保护仅对直流特性严格有效。由于人们越来越意识到这些拓扑效应在物质中的重要性，了解拓扑保护如何在有限频率下丢失是很重要的。这个程序解决了几个凝聚态系统的拓扑不变量的物理利用测量他们的磁光响应在太赫兹频率。该项目还包括设计和实施一套系统的教育光学物理演示和教程，用于培训高中教师和当地K-12学校。

****Technical abstract****This program addresses the physics of topological invariants of several condensed matter systems through measurements of their magneto-optical response at terahertz frequencies. These include the AC quantum Hall Effect in GaAs heterostructures and graphene and the predicted quantized Faraday rotation in topological insulators. Topological insulators are a predicted new quantum state of matter that are expected to have exotic properties including a topologically protected spin polarized conducting surface state, an intrinsic magneto-electric effect and Majorana fermions induced by the proximity effect with a superconductor. Both graphene and topological insulators offer potential innovations in miniaturization of electronics, multifunctional sensor and data storage applications, energy storage, spintronics, and quantum computing. The Hall quantization in all these systems is topologically protected only at zero frequency. The experiments will examine the breakdown of these topological invariants with frequency which is important to our understanding of these important fundamental constraints. The PI has developed unique THz polarization modulation techniques that will allow measurements of the Faraday and Kerr rotation and circular dichroism with unprecedented sensitivity. The program also includes the development of a systematic battery of educational optical laboratory demonstrations and tutorials to be used for undergraduates at the University of Maryland and in the community as a whole.****Non technical abstract****Topology is a branch of mathematics that studies the properties of objects that are invariant under smooth deformations, a classic example being a doughnut transforming into a coffee cup. As in the case of symmetries, topology has profound implications on the behavior of physical systems. Thus the extreme precision of the quantization of the Hall conductivity in the Quantum Hall Effect is a consequence of the topology of the quantized electron states at the edges of two dimensional electron systems. This effect is the basis of the standard of electrical resistance. Similarly topological effects lead to the existence of a conducting metallic boundary of certain insulators. Topological invariants "protect" these metallic boundaries making them good conductors, insensitive to defects and disorder. These topological insulators are a predicted new quantum state of matter that has recently attracted much attention for their predicted exotic properties. However, the topological protection in topological insulators and quantum Hall systems is strictly valid only for the DC properties. Because of the increasing awareness of the importance of these topological effects in matter, it is important to understand how the topological protection is lost at finite frequencies. This program addresses the physics of the topological invariants of several condensed matter systems utilizing measurements of their magneto-optical response at terahertz frequencies. The program also includes the design and implementation of a systematic battery of educational optical physics demonstrations and tutorials to be used to train high school teachers and in local area K-12 schools.