****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.
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.
