**Zoom ID:Â 943 5186 3408, Passcode:Â 627107**

**https://cwru.zoom.us/j/94351863408**

**Theory of quantum anomalous Hall and axion insulators**

Topological insulators are insulating crystals in which the electronic wave functions are topologically twisted in a certain sense. In recent years, a bewildering variety of types of topological insulators have been proposed. In this talk I will focus on two. First, I will introduce 2D quantum anomalous Hall insulators, which exhibit a quantum Hall effect without any external electric field. I will briefly discuss some computational efforts to identify new, higher-temperature realizations of the quantum anomalous Hall state. In the second part of the talk I will discuss 3D “axion insulators” whose surfaces are expected to exhibit a half quantum of anomalous Hall conductivity. While attempts to find examples are still in the early stages, such materials could have strange properties, such as unidirectional electron conduction along the edges where facets of different surface orientation meet.