Symmetries, Dimensions, and Topological Insulators: the mechanism behind the face of the Bott clock

Michael Stone, Ching-Kai Chiu, Abhishek Roy

Published 2010-05-18Version 1

We provide an account of some of the mathematics of Bott periodicity and the Atiyah, Bott, Shapiro construction. We apply these ideas to understanding the twisted bundles of electron bands that underly the properties of topological insulators, spin Hall systems, and other topologically interesting materials.