Geometrical, non-equilibrium and thermodynamic effects in topological systems

In this thesis, I consider three separate aspects of topological phases of matter. Firstly, what happens when they are subjected to periodic driving, using the Floquet theory. Secondly, how the topological classification and the bulk-boundary correspondence depends on the system geometry. Thirdly, what the thermodynamic properties of topological materials are. Here, special interest is taken in terms scaling with system surface due to the topological edge states.