Quantized Electro-dynamical Responses In Topological Materials

The last decade has witnessed an explosion of research investigating the role of topology in band-structure, as characterized for example by the Berry curvature in momentum space in the electronic response of topological insulators (TIs) to Weyl semimetals (WSMs). In this talk I hope to convince you that optical probes of solids give unique insight into these topological states of matter. First, I will discuss how we can probe the special low-energy electrodynamics of 3D TI thin films of Bi2Se3 using time-domain THz spectroscopy. I will then discuss our work following the evolution of the response as a function of magnetic field from the semi-classical transport regime to the quantum regime. In the later case, although DC transport is still semi-classical, we find evidence for Faraday and Kerr rotation angles quantized in units of the fine structure constant. This is consistent with the long-sought axion electrodynamics and the topological magneto-electric effect of 3D TIs. Among other aspects this give a purely solid-state measure of the fine structure constant as a topological invariant. Finally, I will also discuss how optics can observe quantized Hall conductance without involving the edge states. If time permits, I would briefly discuss a new quantized effect in Weyl semimetals.
Main reference: Science 354, 1124-1127 (2016)