Master Defence: Frederik Nathan – University of Copenhagen

Master Defence: Frederik Nathan

Topological Classification of Floquet-Bloch Systems

Topological insulators are characterized by the existence of universal, robust and
highly non-trivial phenomena at their edges. Recently, it has been realized that
periodic driving may provide us with a tool versatile enough to induce these robust
edge phenomena into otherwise ordinary systems. These periodically driven (Floquet)
systems actually have a richer topological structure than non-driven systems, and
for this reason we need to develop a new topological classification. In this thesis we
present a unified and intuitive way of understanding the topological properties of
periodically driven systems. We demonstrate that non-removable degeneracies of the
bulk time-evolution operator determine the edge-mode spectrum of such systems. We
use this understanding to obtain bulk-edge correspondences of Floquet systems for
various cases of dimensionality and symmetry class.
The approach presented here provides a general way of obtaining bulk-edge
correspondences for periodically driven systems. The approach can furthermore
be used to systematically construct Floquet systems that exhibit non-trivial edge