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

*技术摘要*本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，研究了它们的拓扑不变性的物理性质。这些效应包括：砷化镓异质结和石墨烯中的交流量子霍尔效应，以及拓扑绝缘体中的量子化法拉第旋转。拓扑绝缘体是一种被预测的物质的新量子态，它有望具有奇异的性质，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诱导的马约拉纳费米子。石墨烯和拓扑绝缘体都在电子产品的微型化、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。所有这些系统中的霍尔量子化都只在零频率下受到拓扑保护。这些实验将考察这些拓扑不变量随频率的分解，这对于我们理解这些重要的基本约束很重要。PI开发了独特的太赫兹偏振调制技术，将以前所未有的灵敏度测量法拉第和克尔旋转和圆二向色性。该计划还包括开发一套系统的教育光学实验室演示和教程，供马里兰大学的本科生和整个社区使用。*非技术抽象*拓扑学是数学的一个分支，研究物体在平滑变形下不变的性质，典型的例子是将甜甜圈变成咖啡杯。与对称性的情况一样，拓扑学对物理系统的行为有着深远的影响。因此，量子霍尔效应中霍尔电导率量子化的极高精度是二维电子系统边缘量子化电子态拓扑的结果。这种效应是电阻标准的基础。类似地，拓扑效应导致某些绝缘子存在导电金属边界。拓扑不变量“保护”这些金属边界，使它们成为良导体，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极大关注。然而，拓扑绝缘体和量子霍尔系统中的拓扑保护严格只对直流特性有效。由于人们越来越意识到这些拓扑效应在物质中的重要性，理解在有限频率下拓扑保护是如何丢失的是很重要的。该程序利用在太赫兹频率下磁光响应的测量，解决了几个凝聚态系统的拓扑不变性的物理问题。该计划还包括设计和实施一套系统的教育光学物理示范和教程，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.