Frederik Nathan

A thesis for the degree of Doctor of Philosophy defended June, 2018.

The PhD School of Science, Faculty of Science, Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen

Supervisor:
Mark Rudner

Topological Phenomena in Periodically Driven Systems

Periodic driving has recently been investigated as a mechanism for generating nontrivial topological phases of matter within otherwise ordinary systems. Periodic driving can even induce new, so-called anomalous topological phases, which have no counterpart in equilibrium. This thesis studies such topological phenomena and phases in periodically driven systems. The first part of the thesis introduces the concept of topological phases in periodically driven systems, and classifies the noninteracting topological phases that can arise in such systems, including the anomalous phases. The second part of the thesis studies the anomalous Floquet insulator (AFI), which is an example of an anomalous topological phase. The discussion here shows that the AFI is characterized by a quantized, nonzero bulk magnetization density, and demonstrates that strong disorder can stabilize the phase in the presence of interactions. The third part of the thesis explores driving-induced topological effects in other physical systems.
The discussion here shows that periodic driving can lead to new, topologically-robust energy pumping effects. In some cases, these effects can be described as fully classical phenomena and have potentially useful applications. A novel master equation for dissipative, periodically driven quantum systems is derived in this connection.